Condition will I think have an impact on performance but I don't know. If it does have an effect it will be a small effect because everything has a small effect, its the big cummulative effect from many factors we are aiming for.

Condition does have an impact on training. I don't think it has an effect on training performance ie training rate (well, I couldn't find any) but it could. The way condition affects training is if you don't have enough condition to satisfy the expected condition used then you won't get the full gain.

I always aim to have my T11 for a match at between 95-99% (not always possible). I never want my players that gain from training to have more than 94% before the final rest prior to any match. (If they benefit from training I don't like to waste 1% )

NB Just because you think that an effect is small do not ignore it. Success is often found in the aggregation of small gains.