Yes it will work if your Trek is the usual 1 1/8" steering tube(which 99.9% of newish bike are). I use that very extension.
The difference will be night and day, comfort wise.You will have more weight on you butt, less weight on your hands, and your neck will really thank you for it.
You will probably have to change out your cables and housings-unless they are really long.Just the 1st run of housing will have to be changed of course. You can save some $$ by checking to see if your rear housing/cable can now be used for the front.The cable will be long enough of course, but the housing-maybe, maybe not-depends on how the original routing was.
Luck,
Charlie