Hello; well your idea can work and it will not affect the prestashop core or it database since you are using a different prefix for your tables (or just do it without a prefix ).
To Connect two systems here its your Pickup system and prestashop u can merge the two databases via the installation of the module responsible of that, and make the management of the two in the prestashop admin panel...
I'm working on something like that, it may not be the perfect idea but just work on it you may have some good results
good luck