Would regain foam help speed up the growth?

Rogaine will not likely speed up the growth after a hair transplant surgery.  Some doctor recommend it.  It is always a good idea to follow up with your doctor.

You don't need Rogaine to keep the transplanted hair.  Transplanted hair is considered permanent in most individual, but what happens in many people who get hair transplant in their early stage of hair loss is that they lose the existing hair from other areas.  Using Rogaine or Propecia (in men) can minimize that loss and is recommended to prevent shock loss after a hair transplant procedure.

I don't believe that is the case. I still recommend using it though in its more likely role of preserving the remainder of your original hair. There is also a chance of reducing the possibility of 'shock loss' after a hair transplant particularly in women 

There has never been any really good studies evaluating whether minoxidil (Rogaine/ Regaine) helps speed up the growth of grafts after a hair transplant. The general opinion is that it probably does - but doesn't affect the overall results. Vitamins have little role after hair transplantation for most people. 

I have tried this on one side and not on the other side and did this for a year on many patients. The results clearly showed there was not difference between the two side (rogain and not rogain). This clearly shows that this drug does not speed up transplant growth.

We recommend to start on a medical regiment routine after transplant to both slow down the loss of native hair and also help with growth of the transplanted hair.

Rogain is a great product to induce hair to grow longer and thicker. I like to use it on both donor and recipient sites starting two days after the procedure. Secondly, rogain will help the circulation area of the recipient site and will shorten the resting phase of the hair. Therefore I highly recommend using rogain after surgery and if no problems, I recommend you staying on the rogain.