Yes, most definitely... It has effected me in both finding someone to be in a relationship, and being totally open and honest in a relationship. And yes, it can be overcome...
It's had an effect on both finding and being in a relationship, for me. But the people I ended up in a relationship with were extroverts. I think dating another introvert would be much less problematic.
Especially in finding a relationship but also when in one. I've dated extroverts and introverts before. I do prefer relationships with introverts because they tend to be better at understanding that need for space, but relationships with extroverts can work.