It is possible to get a waiver to the requirement to complete disability processing. However, as a baseline, I think you normally could not retire at this point:
AR 635-40:
"3–7. Retaining Soldiers on active duty after scheduled nondisability retirement or discharge date
A Soldier whose normal scheduled date of nondisability retirement or separation occurs during the course of hospitalization
or disability evaluation may, with his or her consent, be retained in the service until he or she has attained
maximum hospital benefits and completion of disability evaluation if otherwise eligible for referral into the disability
system.
a. Officers and warrant officers on extended active duty may be retained on active duty according to the provision
of AR 600–8–24, chapter 1.
b. Enlisted Soldiers on extended active duty may be retained on active duty according to the provisions of AR
635–200, chapter 1.
c. Soldiers in the Reserve Components (other than Active Guard/Reserve) (AGR)) may be retained according to the
provisions of AR 135–381.
d. Reserve Component Soldiers serving on AGR status will be retained on active duty as prescribed in AR 635–200."
Read together, I think this provides authority for normal processing out if you have a pre-scheduled non-disability retirement. As I understand your current situation, you have no such scheduled retirement. So, I think they would look at you as requiring a PEB and a retirement request at this point would likely be denied. Again, there are waiver authorities for the provisions of AR 635-40, and I have seen many things happen that are not supposed to happen based on a strict reading of the regulations. I think I would look at it as unlikely to work, but the first step in trying to accomplish this would be to request retirement. You would likely need to work on a waiver at the same time, though, through the waiver authority for exception to policy.
The waiver guidance is here:
"Proponent and exception authority.
The Deputy Chief of Staff, G-1 is the proponent of the regulation. The proponent
has the authority to approve exceptions or waivers to this regulation that are
consistent with controlling law and regulations. The proponent may delegate this
approval authority, in writing, to a division chief within the proponent agency or
its direct reporting unit or field operating agency, in the grade of colonel or the
civilian equivalent. Activities may request a waiver to this regulation by providing
justification that includes a full analysis of the expected benefits and must include
formal review by the activity’s senior legal officer. All waiver requests will be
endorsed by the commander or senior leader of the requesting activity and forwarded
through their higher headquarters to the policy proponent. Refer to AR
25–30 for specific guidance."
The only other thing that comes to mind is that if you really want to retire, if you talk to your MEB doctor and explain the situation, he may agree to hold off formal initiation of you MEB (perhaps by holding off of the convening of the MEB) until you can submit the retirement request. I still think your unit would have to not have a flag in place and approve your DA 4187.