Is it possible to offset a mortgage with only the appreciation of that property's value?

I'm not certain what you mean by "offset a mortgage" but certainly the appreciation could be more than the mortgage balance. All that means, though, is you now have 50% or more equity in the house.

Say you buy a house with a 100% mortgage for $100k. The house appreciates the next day to $200K. You now own a $200k house and have a $100K mortgage, so you have 50% equity in the house.

If you're thinking that somehow the mortgage "goes away", that's not possible (unless you sell the house and pay it back, of course).

If you mean could the appreciation be more than the interest paid, then yes that's possible as well. If you pay 4% on a mortgage but the value goes up 5% then you have a net gain of 1% (which also is not realized until you sell the house).

Possible? Certainly. That's how some people are able to make money by flipping houses, i.e. buying a house, perhaps making improvements, and then selling the house a short time later for a higher price which covers the cost of the interest payments, improvements, and a profit. However, if the local housing market goes against you, you can end up owning a house that is worth much less than you owe on the mortgage.

Certainly. As a case in point, I bought my house ~10 years ago with 50K down. The mortgage payments are $850/month*, so $102K paid over 10 years. Outstanding balance is $83K, so the total is $235K. In the current market, it would sell for around $350K.

*Numbers are rounded a bit for simplicity.

From your network profile I see you are in the UK. So I will assume you are talking about an offset mortgage as the term is understood in the UK, which is a specific type of Flexible Mortgage where (from Wikipedia) the mortgage holder can

reduce the interest charged by offsetting a credit balance against the mortgage debt, with interest charged based on the outstanding net debt

If that's right, then basically the answer is no, it can't work like that. You need to actually have the cash available for the credit balance; equity doesn't count.

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How offset mortgages work:

Suppose you buy a £300k house using a £100k deposit and £200k mortgage. You know your cash flow is going to be highly variable over the term of the mortgage, with times of plenty and times of scarcity, so you opt for an offset mortgage. This means that in times of plenty you can put surplus cash in the associated savings account, and you will pay interest only on the net debt.

Initially:

Mortgage outstanding: £200k
Associated savings account balance: £0k

Mortgage interest charged on £200k. Repayments bring down the mortgage outstanding amount, but as is the usual case, the first years' repayments are mostly interest

Later, a time of plenty. You put £30k in the savings account.

Mortgage outstanding: £180k
Associated savings account balance: £30k

Mortgage interest charged on £180k - £30k = £150k. Now your repayments are made up of more principal reduction, and less interest, relatively speaking. So the outstanding amount goes down quicker.

What you want to happen:

The house appreciates in value. It is now worth £450k. You want to take this £150k of appreciation and put it in the associated savings account, reducing the amount that interest is charged on to zero, and making your mortgage repayments contribute entirely to principal.

However, where is the money coming from to put in the savings account? It doesn't exist except on paper — you would need to realise the gain, by selling the house, in which case the whole thing's done with; or you could take out a second mortgage against the increased value, but then you're paying interest on that!

So in short, no, you can't use paper profits to offset. Offsetting is specifically for when you're going to have large amounts of cash sitting around.

Appreciation of the house's value is make-believe until you have actually sold it for more than you bought it for, and don't let anyone tell you otherwise. When someone says your house is worth £X more than it was five years ago, that's an estimate, a prediction, a guess. You don't actually have £X more and you won't, at best, until you've sold the house (at worst you never will).

So of course you cannot use this non-existent money to help pay the mortgage — the bank has no reason to assume that you're going to actually receive £X, nor to pretend that you've already handed £X over to them… as such, they also have no reason to reduce your interest.

You can rent part of your property or run a business out of it. In turn using that money to make the mortgage payments. Certainly renting out a room could be able to pay the entire mortgage payment, appreciation of the home and corollary rent market assumed. However this will take time. If you were to lease a room for say 10 years, perhaps that figure if paid upfront could payoff the mortgage. Though you would be required to service the property for those 10 years in the least and have a roommate ofcourse. If it is allowed you could attempt to sell half your property and the proceeds could pay your loan. I can't think of any way without selling part of the property or leasing it. Now if you had a successful online business out of your home and that business was successful it could pay for the mortgage.

At the height of the mortgage madness in the US which led up to the credit crunch, some lenders were offering negative amortisation mortgages, where some or all of each month’s interest was added on to the mortgage value rather than being paid by the borrower, on the assumption that the increase in the value of the property would cover it (but with no thought for how the borrower might eventually pay off the mortgage, whose total balance owed went up rather than down every month). Is that what you’re referring to?