I expect the answer is yes, overhead will increase and performance may be affected. How many additional customers are you anticipating? What I might suggest is creating a test system that mimics this, and then create several new test customer accounts. While this won't exactly simulate a Production system you should be able to get some measurements that will help predict the effects of the increased load. Alongside this it may become necessary to increase resources (RAM, etc) to the server system. This article: https://support.ptc.com/appserver/cs/view/solution.jsp?n=CS185207 is a starting place for troubleshooting performance issues in ThingWorx.
I hope this at least gets you started.
-- Craig A.