Can I store bike inside a regular tent?

The main difference is that the tent gives almost no protection against thieves, where a shed gives a little more protection as it is.
And a shed can be improved a lot with a simple anchor ring which you fix to the ground or through a wall so it is very hard to remove, and to which you lock your bikes.

A well set up tent of a decent quality will keep the rain off your bikes as good as a cheap shed roof, but most tents are not made to do their work months at a time and many will let water through the fabric in heavy or consistent rain, while most sheds, even cheap ones, do a better job to keep the rain out.

Depending on the climate you have where you are, you may find damp inside both the tent and the shed, or more in one than the other, in which case I would expect the tent to be less protection, as most of those are meant for short term use.

A hard layer under or in your tent or even using a tent without build in ground sheet and adding a ground sheet on a hard underlayer will improve against raising damp and keeping water on the ground away from your bike.
But again, a shed will do better and it will be easier to build it up so ground water and rainwater collected on the ground will be kept out.

And a tent which is build good enough to compete with a shed will cost the same as a shed.

For short time storage, like the bikes of visiting friends who are only there for a week at a time, a tent makes sense. But so would any roof, even without the build up sides of a shed, and a well build bike should not get damaged getting rained on, as long as it can dry off properly after a rain shower. Within a tent the bikes may stay damp longer, depending on how the climate is where you are.

Another reason tents are a bad idea for long term storage is that very few will last long in the sun. Canvas is better than synthetic, but would cost more than a shed.

I've had caravan awnings up for months on end, and use groundsheets to cover garden toys, and all go brittle eventually, then tear and fall to bits. Even in my rather cool, damp climate, one summer will probably finish off a tent

For short term storage on a trip, of course you can use a tent, but compared to just leaving them outdoors with a tarp, it offers little, just conceals the bikes.

The one time I have used a tent was when painting the garage where I normally store my bikes. The whole contents had to stay in the garden for a week or two, and some needed the rain kept off

You want to protect your bikes from:

• elements;
• thieves.

A tent offer no protection from thieves, but let's assume it is not an issue. Not all elements are equal.

SUN

A bike can stand UV (the sun) quite long, let's say up to 5 years (especially counting are summers). A tent will not stand that many years (i.e. summers) of UV rays.

WIND

Unless you are living close to the sea, where the air will be charged with salt, you need no protection from wind (ok, wind may carry rain, but then the issue is the rain). A tent would provide superior protection to wind, with respect to a tarp.

RAIN

Very important to protect your bikes from the rain, but a tent would do a job as good as a tarp or a cheap DIY shed

HUMIDITY

This is not the same as rain, humidity makes disaster on rubber and plastic parts, as well as accelerating rusting (usually not a strucutral issue, just an ugly patina ... ugly minus the years when such a patina is cool). You avoid humidity when having enough ventilation. A tent is very bad at this.

SNOW

Snow can do damages as providing water that infiltrates and then freezes (if in your location there is snow, there is cold and there are freezing conditions), breaking many things and displacing any grease you have in bottom brackets as well as in the wheel hubs. And derailleur and gears, poor guys! Tents may collapse and break under minimal snow weight.

WILDLIFE (here only for the sake of brevity, apologize for including them into the elements category...)

Ranging from mice to spiders to killer bees, a tent provide an ideal warm and humid shelter to many companions ... unless you enjoy taking out your bike and a wasp nest, they are not the companions you want for a bike ride start. A tent therefore is not a good idea. This apply as well as to a tarp, although it is way easier to clean it, as well to a shed, but it is easier to place traps and other wildlife repellers in a shed (all these repellers suffers from humidity, while wildilfe generally not, so see point above).

Final point: you can easily store 4 bikes in the tent, but how easy is to take a particular bike out of the tent? This question applies to tarp and to a shed as well, but you can be a bit "rough" with a shed or a tarp, while a tent is easy to be cut/rip, so after a couple of rushed bike extraction maybe your tent is not as effective as it was.