Does Irelia's passive stack with Mercury's Treads?

Solution 1:

Yes

Tenacity stack multiplicatively with other forms of Crowd Control reduction.

Since everything that provides Tenacity right now gives 35 Tenacity, Irelia with any of the CC reduction items will have the following stats

Ionian Fervor stacks multiplicatively with tenacity:
1 champion: 41.5%
2 champions: 51.25%
3 champions: 61%

http://leagueoflegends.wikia.com/wiki/Irelia_the_Will_of_the_Blades

gbn's answer is correct. But I think it's helpful to show the details here.

Solution 2:

Yes, according to League of Legends Wikia because Mercury's Treads provide Tenacity. The same would apply to the other Tenacity items too.

I haven't tested this...