I'm running new hydronic baseboard loops for 1st and 2nd floors.
Can I pipe up to the first baseboard then back down under the floor and then up to the next one and so forth? In other words not in a direct line to and from but dropping them below the floor on both the entry and exit side of the baseboard. I was told if I do that I would cause too much air in the system at the high spots. This gives a nice clean appearance and doesn't require empty covers to be placed over the unfinned pipe areas.

The person who installed mine did that, and it was OK. If you mean what I think - you are just going through the joists, a few inches, not all the way to the first floor from the second?

Piping that way is fine IF you install baseboad tees with manual air bleed valves on the discharge end of each piece of baseboard where the pipe will drop down.
Failure to install such valves can make bleeding the air a real bear.