Will laser therapy help quicken the process of hair growth after transplant?

Lasers do not work to lessen hair loss or shock hair loss.  There is no significant proof on this matter.  It is "safe" to use but it has never been "proven" to be effective.

Laser therapy can help the healing process of the donor area by increasing blood flow and improving the health of the skin cells. Will not prevent shock loss. Also may be used as a preventative for hair loss.

Hair growth after a transplant is dependent on many factors.   These include the quality of the grafts and the treatment of the grafts during surgery.  Where they placed in simple normal saline or was a biologic holding solution used?  Growth factors are also critical for assisting growth after surgery.  PRP, which I recommend with every surgery along with other growth factors can help transplanted hair grow faster and be more robust. Laser can be helpful, but less so than other factors. In terms of shock loss, I find that using implanters makes the most difference.  Typically large volumes of fluid are injected into the scalp followed by the creation of "sites" to place the grafts in.  With the use of implanters, less fluid is needed and therefore less stress on existing hair results yielding less shock loss. 

There are no scientific studies that prove laser helps with hair growth.  Some doctors use laser in combination with minoxidil to help with the growth but again there is no evidence that it helps.

There is no evidence that laser therapy helps in a hair transplant. It is rarely used that way. I have written extensively on lasers, an example article is included in the web reference below