I don't deal with Part 141 but with Part 61, it's really no different. I'll encourage the student to get it done in the first few weeks. Preferably, sooner.
More than anything, I want to clarify there are no issues that may prohibit or delay issuance of a Medical Certificate. That leads to my asking personal questions of the student but it can help begin to fix problems before what does exist becomes worse. Unfortunately, I've seen this in about one out of five students.
Unfortunately the problem is that 141 is different. According to Appendix B to Part 141 (2) “A person must hold (…) student pilot certificate prior to enrolling in (…) the private pilot certification course”. I am told by our FSDO that we have to apply for exclusion. I was wondering how other schools are dealing with that. Well apparently nobody out there is working with 141…;-)