I do not mulch when mowing... A.) because I have an older Deere LX178 that does not have the mulching deck B.) I don't think there is a chute block off for the model deck either.
I 99% of the time keep the deck on the highest cut setting, in the spring/ summer, because I read that taller grass prevents weeds. I did mow it pretty short the last time only because I was going to thatch and spread some fertilizer. There's not much of a mowing season in the Fall here.
By "see how drainage" is going, you may have to elaborate. As far as I'm concerned, if water isn't standing on top of the soil...it's draining. I can only guess that I should be looking to see 'how deep' the water is reaching from a shovel sliced piece of lawn?