Does a Soldier who comes into my command, right out of the IRR for 15 months, get an NCOER with unrated time?

It's not really a gap, the time will be be incorporated into the NCOER dates, but the the 15 months of IRR will get a nonrated code on the NCOER;
The start date will be the day after his last NCOER, presumably the day he entered IRR, and the thru date will be the end of his first 12 months in your unit, or sooner if a change of rater is required.
Assuming he just gets an annual, the dates on the NCOER will encompass 27 months, the rated period will be 12 months, 15 months will be coded nonrated.

CPT,
Take a look at DA PAM 623 - 3 page 157. It is in the back of the reg and describes different terms of service. It states that. "... Periods such as brakes in service or time spent in the irr, ready Reserve, or ing status Are not raible; therefore, these periods will appear as gas in the rated Soldier's evaluation report history."
I can also tell you from personal experience building warrant officer and officer sessions packets that I would come across gaps in NCOERs frequently and when it was due to the Soldier being in the irr I just ensured that that was annotated in their military history. I never had a packet it kick back.

I hope this information is helpful!

HRC may be able to answer that one quickly. Time in the IRR is not likely rated, except when they get orders for some AD.