Can I lose money on a Forex cross currency trade even if the currency pair goes up in value?

My question applies only to cross currency pairs. As an example, imagine my home currency (the currency I am buying with) is USD, and I intend to buy 5 units of the EUR/GBP currency pair. To keep the example simple, let’s also assume zero-spread trade and no commissions whatsoever.
In order to do this, I have to first convert my USD to GBP using its exchange rate. Let’s say, at the moment the order takes place, the GBP/USD exchange rate is 1.39853 and the EUR/GBP exchange rate is 0.86063.

5.00000 EUR -> 4.30315 GBP -> 6.01808 USD

I need to spend 6.01808 USD to buy 5.0000 EUR.

A day passes by and I decide I want to sell back the 5 units of EUR/GBP I previously bought. The EUR/GBP rate has gone up by 2 pips at the time the sell order is put, landing at 0.86083, but the GBP/USD rate has gone down by 15 pips, landing at 1.39703. Using the new rates, the conversions look like this now:

5.00000 EUR -> 4.30415 GBP -> 6.01303 USD

As seen, even though I made a profit from the cross currency pair, as I got back more GBP than I initially spent on the trade, I actually ended up at a loss because the GBP/USD rate went down much more than the EUR/GBP went up, leading to a 0.00505 USD loss.

I would like to know if my example makes sense and if this is a real issue when has to take into account when doing cross currency trading.