I'm assuming that it is a typo / auto correct and the OP meant infected.
It would depend on the relationship I think - given that it is purely hypothetical as i've been with my Husband for 14 years so the thought of being with anybody new is quite daunting.
I'm of the age where we had 'safe sex' drummed in to us (I was 15 when 'Don't Die of Ignorance' was on) so was always very aware of the risks, was very careful but also not irrationally scared due to knowing what had to happen for infection to occur. So, when i was single, I didn't overly worry whether somebody might have it (many did and we're undiagnosed in the 80s/90s) if i wanted to be with them - just made sure condoms were used.
If i'd have felt differently if i'd known for sure, it is hard to say.
I think if i didn't see any proper relationship developing, just a shag, it might put me off a bit as even though it is rare, condoms can break. But, there is also help that can be got if you react quickly should that happen. It's not as bad as it was 2d/30 years ago.
If I really liked somebody, it was going to be a proper, hopefully long term relationship and we took precautions, I probably would yes.