In short, the answer is no.
I'd dare add this small twist, however: the obligations set out by the GPL begin and end when you distribute the software... to your customer. You are in no way obligated to post the source code for the public at large to see. Place it in a src folder as you install it and begone with it; it's there.
In practice, nobody will bother asking you for the source code unless they are a) programmers or b) your competition or c) unsatisfied to the point that they feel like posting it on a file sharing site.
Lastly, as much as you cannot prevent your customers from getting your source code, you can prevent them from getting updated source code (until they pay for it, that is) as you continue developing your app. The part about getting updates is not part of the GPL, and you're perfectly entitled to refuse business from anyone you don't feel like working with.
So at length, no, but with a big twist: it won't prevent you from running a business based on GPL software. And at the end of the day, hey, don't worry about it. It's fun to share code, and there's so much of it around that one more one less won't make much difference.