It's somewhat unlikely. Not having ID isn't a crime in the US, so you can't be arrested for it. Driving is different since you are required to carry a license to drive.

Depending on the specifics of your local laws, it is possible that without ID they may be able to detain you for the traffic violation...but I imagine the paperwork is sufficiently onerous that they wouldn't really want to. Still, as noted above the consequences of actually lying to the cop could come back to haunt you, it's generally best just to accept the ticket and move on with your life. (If you're really cheap, consider taking the ticket and contesting it in court...often times no one will bother to show up to prosecute and the charge will be dropped automatically).