I think EvilC5 is a little mistaken here.
The OP already understands the limitations of clearQAM, since he's clearly using it with TimeWarner. He's only getting the locals with TWC, which is pretty much what he'll get with Verizon.
I'm in the SE Pennsylvania FiOS system ... I think it's VHO8, but I'm not sure. I don't have the eyeTV, but I've run a separate coax to my TV's coax input and I can confirm that I get all of my local HD channels.
But since I don't use it too often (I have the DVR on that TV as well), I cannot say if Verizon plays the same kinds of "games" that Comcast did with clearQAM channels. By "games", I mean Comcast used to switch the clearQAM assignments around all the time. At least once a month. It made for headaches with my Sony DVR for a while. Then, they started pushing through the PSIP data so that my TV and Sony DVR picked up the PSIP mapped channel, not the actual QAM channel.
On my FiOS set-up, the OTA channels are picked up using the PSIP mapped channel numbers.
I think that your eyeTV set-up will work the same with FiOS as it did with TWC. I would expect the eyeTV tuner to be able to pick up all the varied nuanced versions of clearQAM.*
* - If you don't know what I mean by this, what I'm saying is there's at least 2 different kinds of QAM (maybe more). On my Sharp TV, when I auto-tune the QAM stations, there's an option for 2 types of QAM "frequencies", plus an auto mode. I've only ever used auto mode for Comcast and FiOS. I've heard stories where some folks devices (admittedly, this is more than a few years ago) had issues where their TVs QAM tuner wasn't compatible with what their cable system was passing through.
ADDED - another comment. Are you getting a STB/DVR with your FiOS subscription? I can say that if your being offered the multi-room DVR for life, take them up on the offer. In addition to being able to record all of your channels, you'll be able to view recordings on other STBs that you have in the house. It's a really great feature. And don't bother with the digital adapter for secondary TVs. Just pay the extra money for a full STB and save the frustration.