Short answer: no.
Long answer: maybe, but only if the school also has a Letter of Authorization per 91.147 to conduct scenic tours
A "discovery" flight has no definition with the FAA... it's either a flying lesson or it's a passenger flight. Since the scenario is that any random person off the street comes in and purchases the "discovery" flight, that makes the ride common carriage...therefore, there are only two options:
1. The "discovery" flight is a flying lesson, and the pilot needs to be a CFI to log it
2. It's a scenic ride and that requires a Commercial pilot AND the school/operator must also have an LoA per 91.147
Lots of people just use option 1 regardless of the customer's intention...but imagine the scenario where an accident occurs and the FAA questions the customer and they state they bought a scenic ride and had no intentions of taking a flying lesson.... there's a very significant difference as far as the FAA is concerned and both the pilot and operator could be in hot water.
If the flight school is active, already has a good maintenance plan, and has a drug testing policy, then it's probably going to be a pretty simple process to get a Letter of Authorization and be in compliance for those scenic rides...then you'd be legal to give the rides with just a Commercial certificate. So, talk to the operator and see if they already have the Letter, and if not then recommend they get one if they are doing many "rides".