What are the ramifications of delaying the surgery? Discomfort, lifestyle activity limitations?

So your VA funding expires in Aug?

If you take four months off now, that will give you 2-3 months to complete PPL + IR. That's tight but could be done if you can train essentially full time and the school can RELIABLY support your schedule... better make sure of that though.

Also if VA pays for checkrides, those can take additional time to schedule.

If you VA money expires in Aug, I'd be inclined to knock out the training first... that would be a lot of money to leave on the table if you can't get the training worked in before Aug.