You should have no problem with that design based on vent locations.

There may be other ways of doing things that make sense but it is hard to say.

Generally you want the 2 living floors to have their own systems or a way of zoning them. If not you will have temperature stratification problems but the placement of vents is not the issue. Also generally, a basement doesn't need its own furnace. Think what does new construction do - generally there is a unit for the 1st floor that also covers the basement and then there is a unit for the 2nd floor.

Thanks for the reply. I think the rationale we were thinking is that the basement is cool year round and would be too cold if it was air-conditioned. This house has never had AC and I'm not sure the AC will be used more than about 2 months a year.

If it is controlled correctly, the basement won't get the a/c. I have a new house with heat and a/c on basement and 2 upper floors. I'm sure my situation is different but the basement doesn't get too cold and I haven't even installed the zoning controls yet. I just closed the vents as much as possible.