Oh, agreed; it doesn't bottleneck on the connection but instead keeps creating them which can take performance down when you spike. Hence why the original article speaks of using something other than a RDBMS, such as Dynamo, since there really is no way of addressing that issue (since you can't set a concurrency limit on one kind of function; else you could have one function that has high concurrency invoke one that is far lower, that exists just to keep connections pooled).

If you absolutely must hit an RDBMS, be quick about it to free up the connection, and definitely consider if the latency matters that much; a few dozen ms more to initialize and close the connection is going to be a LOT cleaner.

But that said, how badly it penalizes you for scaling connections up depends on the DB.