it is possible but:

• you need to have a cluster running all the time. Sql serverless spins up fast, but it takes several seconds nonetheless which can be too long of a wait for a web app.
• calculate the cost. It might be cheaper to run a classic RDBMS
• think about optimizations that might be necessary for your app (indexing mainly) that are not always possible in databricks
• do not forget labour cost for maintenance/development (this is probably a pro for databricks)

I might think of more things later.