Well, sometimes. :)
If the guy's genes don't work with *anyone*'s genetics -- this is the part of the human genome that is varying the most, changing the quickest under selection pressure, so a lot of guys have variant sets of instructions for implantation -- then a surrogate might also be at risk of HELLP.
If the guy's genes don't work with certain genetics, then it depends on the surrogate. One who can work with him won't have issues. One who cannot work with him will.
The really odd thing about this is that it's true even if you use one of your eggs. Your eggs would encode for half of the baby's genes -- so the baby would be entirely the product of you and your partner. But the part of the blastocyst that goes on to develop into the placenta is all paternal. The maternal genes are epigenetically silenced. Those paternal genes work with the genes in the uterine lining -- the decidua -- to form the placenta.
So the genetics of the surrogate also matter, because they will direct the development of the placenta while the genes carried in the egg direct the development of the fetus.