Some tables are based on arrival time at the stop rather than time leaving the bottom. In that case it doesn’t matter what ascent rate Ian used so long as it is lower than the maximum. Mor3 commonly it does matter.Yes, they can, but it gets complicated because the response is really different from different situations.
1. If you are diving using the old system of tables, the tables assumed you were ascending at a certain speed. If you start the ascent near your NDL but ascend slower than the tables call for, you could well have a decompression obligation as a result without knowing it.
2. If you are instead using a computer and ascending very slowly while staying within the NDLs according to the computer algorithm, you are OK.
3. If you are doing deco diving with a software-based dive plan and ascent too slowly to your first scheduled stop, your decompression requirements will have changed as you ascended. As an example, I recently did a technical dive on a wreck, and nearly all the dive teams reported nearly identical dive plans, and every team was using the same computer algorithm. My buddy and I arrived at the ascent line just ahead of the last team to ascend, a team I knew was using the exact same dive plan and the exact same dive computers and settings we were using. When we reached our first decompression stop, I looked back down the line, but they were not in sight. I did not see them emerge from the gloom for several more stops, and they ended up doing 10 more minutes of deco than anyone else did. When asked what happened, they said they did not know--their computer had just kept adding time. I pointed out that they had ascended very slowly from the wreck, and they said, "You're supposed to ascend slowly." Well, the computer wanted them to ascend at 30 FPM, and when they were slower than that, the computer added more decompression time. They were lucky they were using computers. If they were simply following a schedule and then ascending slower than the schedule called for, assuming it did not matter how long it took them to get to the deeper stops, they might have gotten bent.
Divers are generally poor at keeping to the default rates and so computer generated plans are often wrong. You ought to be able to tell though. If the arrival time at a stop is, for example, 60 minutes and you get ther at 63 minutes you are no longer in plan and need to move to a contingency. This should not happen, but it may require altering the default ascent rate to be realistic or going faster.
General paranoia over going up too fast means that actual dives are usually much slower than planned unless the diver has realised and made an appropriate plan.