Hello Max,
As far as I know, IRCC is letting students start their studies without aips or visas for now as processing times are delayed due to covid. However, if your college says you've passed the deadline to submit your visa, you may have to defer your intake to May.
In my case, our university gave us time toll April to submit our visa approval. Please check with your agent or student coordinator.
Also, no it won't affect your ppr. Once you sharw the revised LOA with IRCC, they will update your file and automatically your ppr will come in time for May if you choose to defer.