It can. Ideally, the same phone number will always be displayed, but in your case (and a few of my clients), dynamic call tracking really needs to be on the site.
There are solutions to this. I don't know which software you're using, and it could differ depending on the software. The solution we found that worked was to put the call tracking script in, and have it change the phone number on the website only when traffic is coming in with certain parameters.
This works well with PPC call tracking, because the traffic coming in has predictable parameters, and those can used as a trigger to fire the script. Search engines aren't going to use these parameters, so they won't effect local SEO. Depending on how much direct and referral traffic you have, you might be able to use this solution with your PPC pool of numbers, and then you can focus on separating the referral and direct traffic from the SEO traffic to get the data you need. We usually only split the PPC traffic this way, trying to do it with organic could get you into trouble.