Will I be made to sign a waiver before enlisting due to multiple tattoos (all hidden by clothing)?

Most likely. However, your recruiter should be able to provide you with accurate information as generally speaking you disclose this information when you begin the enlistment process. When I signed my contract back in November, a guy who failed to disclose a tattoo (minimal in size, by the way) under his armpit, was rejected by the MEPS personnel.

So.. Talk to your recruiter!

Will this be an issue getting in the army?

The regulations for 670-1 have changed a lot recently. Under the most recent changes tattoos that are visible when when wearing short sleeve APFU and shorts require documentation. If your ink is all above the bicep, below the neck, and above the thigh there shouldn't be any complications

The regulation on tattoos seems to change frequently. However, currently the amount of tattoos does not matter as long as there are none on or below your wrist, head, or neck. Also keep in mind they cannot be gang related, nudity, sexist, racist or any other extremesist type dialog. Currently if they are within those guidelines you will not need a waiver. However if they are not, you will. How that helps answer your question.

Regardless, be proud of yourself for being willing to step up and serve.