Obviously if you spent a considerable amount of time chasing strength goals, you will develop some muscle in the process. It doesn't however always guarantee the best looking (or even largest) muscle in the process. There are plenty of bodybuilders whose muscles (even their legs) dwarf those of powerlifters. (I'M NOT SAYING THAT THERE AREN'T SOME PLers WITH HUGE MUSCLES)
The best way to gain size is to train specifically for size. However, as your short term goal is strength based, I would suggest tackling that, albeit keeping in mind that you may decide to try your hand at bodybuilding at some point, and don't allow the development of huge imbalances.
Now, do people win shows with huge legs? Absolutely. Do people with huge legs and severely lacking everything else win shows? Nope. I've gone up against some guys whose leg size just dwarfed mine. Personally, I can admit that my quads were always a weak point. Still, despite this situation, I've beaten other competitors because they weren't up to the same standard in every other area of their physique as they were with just their lower halves.
When you hear people talk about how 'legs win shows', or 'contests are won from the back', it's not because the judges are only looking at those bodyparts, it's because at a certain level, everyone is of an especially high caliber of development, and these two muscle groups tend to be the deciding factor between already excellent physiques.
IMO, if you don't completely neglect everything else while chasing strength goals, I can't see the transition being too much of a problem.