HI Matt
Ok well based on what I have seen recently at customers this depends a lot on the type of tile, whether it is calling a OData service, how well that OData service performs, & what caching you are using.
Eg if you are using Smart Business Tiles you really want to be using the associated caching mechanism... Which means being on the appropriate SAPUI5 release ... Which as I recall is 1.34.
I haven't seen any good rules of thumb yet...because it is so dependent on which tiles, which OData Services, what caching mechanisms, etc.
From a UX strategy point of view I would suggest being very cautious about how many tiles you put in the initial group of the launchpad anyway. Information overload can be a bigger problem for users than performance load. Sure sign of lack of UX design is a dashboard of random just-in-case tiles. Dashboards need to "tell a story" too ... Eg is today going to be a good day?
(suspect I am preaching to the converted here but for the benefit of others...).
Hope that helps a little
Jocelyn