Yes, failure to register is a serious criminal offense on its own, and prison is absolutely a possible outcome. In most states, failure to register as a sex offender is charged as a felony, which carries the same weight as any other felony conviction. The severity of the charge and the sentence range depend on the state and whether it is a first failure or a repeated violation.
The situation becomes significantly more complicated when the person is already incarcerated with a bond. If they were released on bond from a prior case and then failed to register, the failure to register is a new criminal charge on top of any existing case. The bond from the prior case will almost certainly be revoked, and they will face prosecution on the new registration violation simultaneously.
If they were released early on the original sex offense and the failure to register constitutes a violation of the terms of that release, they may also be sent back to finish the remaining time on the original sentence. That is separate from any new sentence on the registration charge. Both consequences can run at the same time.
Sex offender registration requirements exist precisely because the courts view non-compliance as a public safety issue. Judges treat registration violations seriously and are unlikely to be lenient in a case that involves both incarceration and a bond, which already signals a complicated legal history.