No, it's not a bad thing.
It's rather question of number of parallel connections in total. This can be defined by "max_connections" in mysql settings (default it's 151 since MySQL 5.1.15), and is limited by capability of your platform (i.e. 2048< on Windows, more on Linux), hardware (RAM) and system settings (mainly by limit of open files). It can be a bottleneck if you have many parallel users, number of databases is not important.
I made a script which connects 400+ databases in one execution (one after one, not parallel) and i found mysql + php handling it very well (no significant memory leaks, no big overhead). So i assume there will be no problem with your configuration.
And, finnaly - mysql_pconnect is generally not good think in web developement if there is no significant overhead in connecting database per se. You have to manage it really carefully to avoid problems with max_connections, locks, pending scripts etc. I think that pconnect has limited use (ie. cron job runned every second or something like that)