Is it possible? Could you build size and strength while having good cardio and hand speed?
Would doing a strength/bodybuilding routine like Madcow 5x5 3 days a week and boxing the other 3 days be a good idea? Assume I get a minimum of 8 hours of sleep and eat everything in sight. I don't plan on being competitive in either, just good.
My current lifts are
No boxing experience
It's possible, but mind that you are doing two seperate things. Especially in the beginning you will need time to adapt your muscles (resting time) or you're in for overtraining. So start it slow, because in running/cardio it's about strength per weight and you need to get in slowly.
Furthermore you'll nee more Springiness. The good news: Maximum strength (i.e. lifting) is somewhat the lower bound of the springiness you can devellop: No muscles, no springiness.
The bad news: more muscles doesn't automatically mean more springiness.
Frankly in any grappling style you would probably have more carry over from your training, but boxing is a great sport, so have fun.
Just in general:
Power lifting adds a lot of bulk that won't really help you much in terms of technique or power because your footwork, hand speed, and timing are more important anyways. You will be stronger, but if you're not training for boxing, your power will most likely be wasted since you'll just be bigger and more clumsy than someone else in your class.
Don't get me wrong though, strength training with boxing training is a phenomenal combination.
Hybrid Pause Squat 5x5
Pike PU/Push-up 2x4-15
Bodyweight Row 2x4-15
Single Leg Step ups 2x4-15
Front Pause Squat 5x5
Bench Press 5x5
Bodyweight Rows 2x4-15
Box Jumps 2x4-15
>>Power lifting adds a lot of bulk
Nope, power lifting while eating a fuck ton adds bulk. Powerlifting, like boxing, is a weight class sport, you can get stronger while staying the same size.