Yes, you can. Wind management will be something to consider for noise, even if lift isn't a factor. A simple fairing made of plastic, ABS, etc. will usually cure any issues.
At one point I had a panel mounted on crossbars on the forward area of my roof:
I added the fairing right after mounting because of the aforementioned wind noise. One note here: My fairing was made by just putting a stainless hinge on a piece of ABS and letting the other end flop down onto my fiberglass pop-top roof. This movement did cause some abrasion in that spot, so either I should have added some clear 3M protective tape to the area, or rigidly mounted the fairing up a bit so it didn't rub.
I have since moved the solar panel to the rear of the roof (because of the physics involved with the pop-top), but it is still mounted to cross bars:
I've mounted panels a few different ways, but I always prefer a method that makes it easy to remove the panel for optimal sun placement. So rather than mounting the panel directly, I always make an outer frame from either C-channel or angle aluminum. The frame hard-mounts to the roof bars and the panel slides out on plastic runners and can be locked in place. Here's a mid-construction shot of my latest frame
The long sides are 1.5" angle, the ends are 2" C-channel with some shims. One and is fixed, the other hinged so when I close the frame it grabs the panel on top and bottom making it physically secure and giving me a place to put a padlock:
Hope that helps.
EDIT: I should have mentioned that I use crossbars made by Surco. They're steel bars with an extruded profile that gives them T-slots on top and bottom. I had Yakima bars in the past and I find the Surco bars much easier to build mounts for because I can just slide 1/4-20 T-nuts into the slot and drop a bolt anywhere I need to. Think of it like a single-bar version of the flexibility of a T-slot roof rack. With solid round or square bars, you can sort make it work with the wrap-arounds, but you have to figure an offset and then you have a piece of plastic in the mix (or you have to find/make a metal "wraparound" equivalent).