Can you mobilize on a profile?

You may not be allowed to come into active duty from the reserves on a temporary profile. You can do so if you have a permanent profile though. See AR 40-501; it also depends on the PULHES and the job you'll be doing. Your commander will be the ultimate authority on that.

A. Profiles. Medical guidance is critical in advising commanders of potential problems, physical limitations and potential situations that could be harmful to the Soldier or detrimental to the mission.

Medical determinations and recommendations to commanders are provided in the form of physical profiles documented on DA Form 3349, Physical Profile, after evaluation by a health care provider (HCP). Some Soldiers, because of certain medical conditions, may require administrative consideration when assigned to combat areas or certain geographic areas.

B. Profile violations. Determination of a Soldier’s assignment or duties is the commander’s responsibility. As such, it is a commander’s responsibility to counsel Soldiers on those duties they may or may not perform while deployed to combat areas or certain geographic areas. The Soldiers will be advised they will not violate their profiles and will perform duties assigned by the commander which they can perform without undue risk to health and safety.

C. Temporary Profile. The final decision to deploy a Soldier is a commander’s decision, based on the HCP recommendations and taking into account the mission requirements, geographical and environmental conditions the Soldier will be subject to.

A Soldier with a temporary profile may deploy after the profile expires or when the commander and the HCP agree the Soldier is deployable.

D. Waivers. When HCPs and unit commanders disagree on the deployability status of a Soldier, the decision will be raised to the first general officer in the Soldier’s chain of command, who will review the case and make the final decision.

For Soldiers with any of the conditions listed in current Department of Defense guidance or the combatant command’s published medical screening criteria, the general officer recommending deployment must submit a waiver request through the COCOM surgeon to the combatant commander for approval.

The decision must be up to the unit then, unless I missed something. I'm currently deployed and this unit was told outright, "soldiers on temporary profile will not deploy". Also, right now any soldiers who "slipped through the cracks" are being found out and sent home.

It shouldn't affect your mobilization. I would get one because the longer you let something set the worse it gets.