I had the same issue arise. My Dentist thought I might need 1 possibly 2 root canals. I called and spoke to our Nurse at the IVF Clinic and she said that yes I should have the work done and preferably before the transfer. But of course my transfer isn't for couple of weeks, so it may be differnet as yours is coming up fast.
The risk is that the tooth can absess and become infected (very painful, and very serious if it gets into your blood stream). My dentist will not perform any work in the 1st or 3rd trimester unless it is an absolute emergency.
If you can get cleared to do it tomorrow, I definitely would.