The short answer is yes, it could have an SEO benefit but I would think carefully about the impact on the affiliate campaign.
The major advantage of being on a major affiliate network is the access to thousands of affiliates, some very large ones. If you took this is house you would need to put a lot of resources into recruiting new affiliates and even then you might not find the quality of affiliate you would get on a major network.
If you took it in house there is of course the tracking, admin and payment side of the affiliate setup to consider, implement and apply resource too as well.
If you (or your client) is serious about the affiliate campaign then I doubt you would improve it by taking it in house.