No, seeing the screws wouldn't bother me. It's traditional. But I would probably go around and make sure all four slots in each plate were facing the same direction.

Aren't you building a Georgian/Federal revival?

A large escutcheon/sideplate wasn't really typical. They usually had a knob and small rose with a separate keyhole that all looked rather small for the door to modern eyes. (At least after they started mortising the hardware into the door and not using box locks)

Not at all, classic style. That's what the original plates look like in my 1912 house.

It's part of the design. Just be sure to get matching screws. Non-matching screws would bug the heck out of me.

Matching screws are a must. After living with them for 2 or 3 weeks, you won't even notice the screws anymore (if you ever do!)

LOL!!all four slots aligned!
I'd probably do the same thing...9:00 & 3:00

If they were Phillips screws, probably would bother me. Should be slot head.
Casey