NO, I DON'T think stress affects conception. And I will punch the next person that tells me to relax and it will happen.
I was very, very relaxed the first year we tried, I didn't have high expectations of getting diffed immediately so we just had fun for a year. No temping, no opks, no monitors, just relaxed fun. I didn't get pg. Roll on to 19 months of trying and I'd starting tracking cycles and obsessing over everything, symptom spotting, crying when AF arrived etc. I'd had a ridiculously hectic and stressful end of summer term at work, a trying encounter with the MiL, a long haul flight that came after a missed coach to the airport, a taxi chase across the country etc etc and then no luggage on arrival. For two days. Including the tent we were supposed to be camping in. I was very stressed and not remotely relaxed. This was the cycle I got pg!
If you are very stressed to the point that your periods are affected then obviously that will affect conception. If you're constantly tied in knots with anxiety etc then that will affect your whole general health including fertility. People are always full of anecdotes about women who got pg when they 'stopped trying'. Bollocks, no-one just stops trying unless they've started using contraception. And if they didn't have identified fertility problems maybe it just took them longer to get pregnant - anything up to 18 months is still classed as 'normal'. How do you explain rape victims who get pg? Women in refugee camps? War zones? Times of famine? None of these women would get pg if stress prevented pregnancy.
Having had my little rant, I do think a positive outlook helps, and relaxation is always a good thing, but telling women that stress affects fertility is A) implying it's their fault and B) will make them more stressed. Fertility is a very complex thing, there are so many factors that could be affecting your chances. Even if stress is a contributing factor it's incredibly unlikely to be the sole reason it's not happening.
^^