Here's what'll happen:
Until Singed gets his lvl3 poison and at least champ lvl6, the fight could go both ways since both champs are basically melee. Probably will just try to stay out of each others way, although Irelia can put more pressure on because she can stun and land some free hits on Signed without worrying too much about the weak poison.
Then, from lvl6 on both champs, there's really no way that one or the other will be able to kill each other if they are both careful. If Irelia gets too aggressive, Signed will fling, goo, gas and potion away while regenerating health. If Signed gets too aggressive, Irelia will stun, ulti him in the face while healing and gapclose away if needed.
Mostly, they will just be hating on each other the whole time but never kill each other. Signed has an easier time farming, but Irelia has easier ways of regenerating her health, so she can ignore the occasional Signed aggression and still keep on farming. Ultimately, the ganks from teammates will decide who wins the lane