Yeah, you just have to use a little bit of force to get everything to line up - it's not going to damage anything.
As for "what if I don't".... well, it depends on the orientation and the specific card.
A (relatively) heavy GPU, and a vertically mounted motherboard, you run the risk of damage to the PCIe slot, or a loose connection with the pins not making full contact; as a result of the weight of the card..... but provided you don't move the system, it *should* be ok, but there's no guarantee.
Looking at the picture, you don't have any major problems there - that's typical mounting. I'd just put the screw in (again, with a little force) as is intended. While the risk of damage is fairly low, it's just not worth the hassle not...