This will depend on the computer. Shearwater, for instance, computes the ceiling expecting that you will ascend at 10 m/min. As such, you would always have that stop if that recommended ascent rate is followed. Other computers may vary in their ceiling calculation.it is possible that following the computer's recommended ascent rate will clear that decompression obligation along the way.
Now, going slower than recommended (what I suspect the OP did) is complicated. The stop time may reduce or even clear (e.g., a fast tissue dominated and the ascent speed was still fast enough to avoid excessive loading of the next tissue). In some other cases, the stop time will definitely increase. All in all, I think it's best to follow the computer as soon as the inadvertent deco is discovered.