Possibly, but the evidence is thin. The best-known study followed nine men doing four minutes a day and reported thicker hair in that group. Nine people is interesting, not conclusive.
Transcript
The honest answer is a maybe, and the evidence is thin. The best known study followed nine men doing four minutes a day. Nine. Hair got thicker in that group. That's interesting. And it is nowhere near enough to build a plan on. Massage is free, and it won't hurt you. Just don't let it replace finding out why the hair is going.
Massage is free and it will not harm you, so there is little reason to avoid it. The risk is opportunity cost: months spent massaging are months not spent finding out why the hair is going in the first place.