Does using Estimated Breeding Values cause the Inbreeding Coefficient to increase?

The short answer is – no.

It is not the use of EBVs that causes inbreeding to increase. Rather, when dealing with a small, closed (or mostly closed) breeding colony, inbreeding will increase regardless of whether or not the decision-maker uses EBVs to identify a subset of young males and females to become parents of the next generation. The smaller the effective population size of the breeding colony, the more rapid will be the increase in inbreeding.

Also, remember that inbreeding increases as generations turn-over. The shortest generation interval in dogs is about 2.5 years, but it can increase to a much longer interval by keeping females too long (usually beyond 4 years of age) and by using a small number of males to produce a large number of litters over 6, 7, or 8 years. Breeders sometimes keep males intact and allow them to breed over many years, but from the population perspective, this “kills” genetic diversity. 

Thank you to Dr Eldin Leighton for your insight into this question!