40+2, Third time mom breastfeeding?

Ok so our situation is a little different this time...this will be our last baby due to medical issues. So I am having my tubes tied 24 hours after delivery.

My son will be with my husband obviously, but I’m a little worries about feeding during this time. I over produce a lot of milk I have with both of my previous pregnancies and I leaked about 2-3 oz during my last labor. However, the dr said that is no guarantee that I will do so again this labor in spite of the fact that I am leaking a good amount of colostrum randomly...

So....the doc mentioned I pump a little prior to going in L&D so that my son will have something to eat just in case I don’t get out of recovery and he ends up hungry. I’m scheduled for induction next Friday 4/12 but I’m also 40+2 and 4-5cm dilated and 100% and had a sweep on Tuesday. I’m having consistent contractions just not strong enough yet.

Should I go ahead and pump a little to have just in case I go into labor before next Friday? Doc gave the ok, Just is that too early? Also will this increase contraction intensity?

Thanks girls!!!