And while it's been a few years since I last read Carey's "Captain April" novels, I remember them well, and don't recall any major conflicts with present canon or novel continuity.
I've already pointed out the big one: They use the SFC timeline and put TOS six decades too early. And in skimming through it, I was reminded of several others. For instance, Final Frontier makes the odd claim that April's Enterprise was the first vessel to be called a "starship." It claims it was the first ship to be capable of continuous warp travel instead of successive short hops, making it some seven times faster than any other ship. It claims that transporters have only just become practical for human use. (Heck, a lot of this didn't even fit together with The Final Reflection, another book that was based on the SFC timeline.) Basically it's a lot like what Enterprise did a couple of decades later with NX-01, only it's putting those "first-time" breakthroughs just a couple of decades before TOS rather than over a century.