No. There may be an issue with inbound flow rates,but that would be dependent on the capacity BHD has whilst they are using procedural control. Those rates would be set by BHD and Flow control. If NATS at BFS are doing radar for them then there should be no difference in normal flow rates.
I don't know if NATS has taken over the provision of radar services yet. I expect they haven't as BHD seems to be operating a fully procedural system. I doubt that NATS is using the BHD radar. The BFS radar has a reasonable level of coverage at about 10/12 miles from touchdown on 04 but that degrades as the aircraft descend below the level of Divis and Black Mountain. The ideal solution is a radar feed from BHD into BFS.
That may be a proposal which is under consideration.