Yes, by the standards of PADI, SDI, SSI, NAUI, GUE, and any other U.S. agency that I know of, recreational diving does not include any decompression other than that which occurs during a normal, continuous ascent and an optional safety stop. Diving that has mandatory deco stops during the ascent is classified as technical diving.
I specified U.S.-centric because it is my understanding that at least one European agency (CMAS?) has a level of certification that includes training on limited decompression that is still classified as "recreational" and not "technical".
And, yes, as far as I know, any recreational-oriented dive computer will still calculate deco stops if you stay down past your NDL. But, I would not recommend to anyone to use one of those if their intention is to actually do decompression dives. The reasons why are too long and OT for this thread. There is a reason why those computers' manuals generally tell you that if you exceed your NDL you should do the stops that the computer tells you and then stay out of the water for at least 24 hours afterwards.