A couple of points then.....

No, pushups do not work your max strength. Not directly. A man who does pushups all his life will be able to bench press more than a man who doesnt, but thats just down to stimulating muscle fibers full stop. When you get specialist like we do there are a number of factors concerned.
Why ask if theyre any good, when pushups work muscular endurance, core stability, explosiveness and speed. (with the variations)

Of course if max strength is your main goal, then get off the floor and get onto that bench, but they can be beneficial to boxers.

There is an ever-ongoing argument about the best way to improve your max strength.
Theres the hardcore powerlifters, 1 rep maxing all day, then theres the strength trainers, using programs like the 5x5(look it up, an EXCELLENT (some argue the best) strength training program)

One thing remains constant though, and thats the use of compound and olympic lifts for strength. You want to get strong, squat, deadlift and clean and jerk till you cant stand.

Then, last point, we employ fast twitch muscle fibers by moving heavy objects, fast. EG clap pushups or SHOTPUTTING. We need fast twitch to punch harder because thats exactly what your hand is doing, moving fast.

A shotputter throws a 10lb ball for three months, records her distance at the end. She then moves up to a 15lb ball for three months. At the end of the three months she then throws the 10lb ball again, guaranteed that that ball will go further (disconcerning other minor factors)

I know somebody who bench presses explosively (yes, he is crazy) and he says it is phenomenal how much everything has benefited. His max strength is going up, aswell as his punch power and general power overall