My friend in Houston is trying this right now but it's incredibly stressful. A lot of companies aren't interested because he's unsure whether he's even coming to their city, some are turned off because they assume he'll want relocation, not to mention it's emotionally trying for him to hop from city to city for interviews and not even know where he wants to settle.

There is also a cost of companies having to fly you to interviews using this strategy, so I guess it will make things a tiny bit harder.