Is it possible for me to make O-6 if I go before the promotion board next month and my MRD is just under 3 years away?

Does age play a role in this sir (e.g., if the soldier will be 60 at MRD)?

LTC (Join to see) - Yes, but not in your example. The maximum age was raised to 62 for most officers back in the early 2000s. However, to your general question, both (maximum age and MRD) are "whichever comes first" type of maximums.
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* 10 U.S. Code § 1251 - https://www.law.cornell.edu/uscode/text/10/1251

COL Randall C.

Thanks sir. Another question concerning retirement rank: if an O5 is promoted to O6 and is in that grade for 2 years 2 months, at which point that officer hits MRD and is forced to retire: what rank would that officer retire at?

LTC (Join to see) - O6.

If you were voluntarily retiring before your MRD it would be three years, but for officers and enlisted who are involuntarily separated, the requirement is 185 days or 6 calendar months (10 USC 1370a*).

Paraphrase of 10 USC 1370a(c), Service-in-grade Requirement for Offices in Grades Above O–4 - normally a reserve commissioned officer must have satisfactorily served an active status for not less than three years. However, that officer can be credited with meeting that requirement if they have completed at least six months of satisfactory service in that grade and is being discharged solely due to a nondiscretionary provision of law requiring the discharge due to age or years of service.

Multiple ARs address this in some form or fashion:
• AR 15-80*, para 2-3
• AR 135-180*, para 4-6c
• AR 600-8-24*, para 6-1
• AR 600-8-7*, para 6-3c
etc.

This assumes that the officer doesn't have any 'dings' that would require them to go to the Army Grade Determination Review Board because a period of their service might be unsatisfactory (if they haven't been in trouble, then they won't go through the determination).
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* 10 U.S. Code § 1370a - Officers entitled to retired pay for non-regular service - https://www.law.cornell.edu/uscode/text/10/1370a
* AR 15-80 (Army Grade Determination Review Board and Grade Determinations) - https://armypubs.army.mil/epubs/DR_pubs/DR_a/pdf/web/ARN11826_AR15-80_FINAL.pdf
* AR 135-180 (Army National Guard and Reserve: Retirement for Regular and Non-Regular Service) - https://armypubs.army.mil/epubs/DR_pubs/DR_a/ARN33567-AR_135-180-000-WEB-1.pdf
* AR 600-8-24 (Officer Transfers and Discharges) - https://armypubs.army.mil/epubs/DR_pubs/DR_a/pdf/web/ARN3140_AR600-8-24_FINAL.pdf
* AR 600-8-7 (Retirement Services Program) - https://armypubs.army.mil/epubs/DR_pubs/DR_a/ARN30707-AR_600-8-7-000-WEB-1.pdf