Yes it happens, Pilots are reluctant to hold enough aileron into wind to keep the upwind wing down on the roll because of fears of spoiler drag. As soon as the wheels leave the ground, the upwind wing has far more lift than the other and will roll downwind, requiring suddenly far more into wind aileron. Then the weathercocking effect takes effect because as the wheels lift off, you are instantly sideslipping. On the 747, the effect can be startling- I've seen 90 degrees aileron instantaneously applied into wind to correct the situation. I've been watching and sometimes suggested in strong winds further aileron would be a good idea. When it's not, it's interesting to see the result! I even once witnessed a pilot who didn't apply any aileron on the roll in a fresh crosswind- I think he learnt the point quickly, but I wondered how the training section hadn't picked this up in the simulator.
The same effect seems less pronounced on the 737.
It sounds arrogant, but it's the one place I disagree with Boeing on crosswind take-off recommendations. Spoiler drag below about 120 knots is, I believe, irrelevant. The spoilers aren't even that good for slowing jets up below 250 kts, so partial displacement below 120 kts isn't going to amount to more than 'a hill of beans'! Partial spoiler drag on take-off has little effect. But the BFCTM says otherwise.