Mooring pennants are relatively thick lines with a float at one end and attached to the mooring at the other. The bowthruster channel is below the surface, so it cannot pick up either end. I have a big bowthruster with a 25cm diameter (10 inches). It is very difficult (polite phrasing for "impossible") for the typical BVI pennant to naturally bend at 180 degrees in a 10 inch radius and get sucked into the bowthruster tunnel. Bowthruster tunnels generally do not have screens - they really are not needed. Smaller boats have even smaller diameter bowthruster tunnels (6-8 inch) and they could only ingest an end of a line, not a loop in one. Plus if you aren't alone you'll have someone on the bow and I recommend using hand signals rather than voice. Have them point left for you to move the bow left, and point forward to move the boat forward and make a fist straight up for you to stop the boat. And a happy thumbs up for having attached the boat to the pennant on a cleat, letting you go forward to either approve their efforts or clean up the attachment. If there's a chance of ingesting a pennant while picking up a mooring, they would just use the appropriate hand signal to stop. I've been using that method with uninitiated newbies on crew for years and we have rarely missed a pickup.

A bowthruster is a wonderful tool which makes lots of close-quarters actions much, much easier. If you have one, use it!