It's pretty straightforward to work the numbers.
First, when an uninformed tech gets lube in the piston head filter, flow usually doesn't completely stop, but just slows down. When flow drops from the specified 26ml/min down to say, 6 ml/min (as I've seen many times in eBay regs), the depth compensation doesn't stop. It just slows down.
So let's make some assumptions...
If the volume of the ambient chamber is 5ml, it will take 5/26 minutes, or 12 seconds to double in pressure during descent. That means you'd need to descend from the surface to 33 feet in 12 sec (>150 ft/min) to overcome the ability of the old Sherwoods to keep up.
So if your clogged filter was down to 6 ml/min, descending at 25 ft/min would still be okay.
If you descended at 60 ft/min, your relative IP would begin to lag.
In the worst case scenario, a completely clogged filter with a perfect bleed valve would lose 15psi of relative pressure every 33 feet.
In other words, at 132 feet, the ambient chamber would still be at surface pressure (15 psi), while ambient would be 75 psi.
Thus, your operating IP would be 135-60psi, or 75 psi.
Most balanced second stages will barely register an increase in cracking effort at 100 psi. An old center balanced second like the D400, or my new TFX, won't even notice it. At 75psi IP, cracking effort begins to rise for barrel regs, but not for center balanced valves.
In fact my new TFX, initially tuned to 0.9" cracking effort, will still crack at only 1.4" at 20 psi IP!!!
So with a non-functioning filter, I'd barely notice a problem at max recreational depth.
Of course, there's more to the issue. It's not just cracking effort, but dynamic flow. At 75 psi static IP, there might be a bigger drop in delivered IP during a breath.
But the point is, you're not gonna die due to your tech's excessive lube clogging the filter, even at max recreational depth. And since the bleed valve is never perfect, the reg will flood and the ambient chamber will not stay at surface pressure, but will instead lag just a bit behind actual ambient during descent. So your cracking effort and dynamic IP will be even better.
Yes, you'll have to service your reg for flooding after the dive, but absent unusual circumstances, you'll make it back to the boat alive.
It all depends upon the second stage. In the worst case - an unbalanced second, everything is IP dependent. Here there might be a problem. I measured my old Cyklons in this regard, and they're illustrative.
The Cyklon's cracking effort will rise about 0.2" WC for every 10 psi IP drop. With a Cyklon tuned to 1.0" cracking effort at 160psi IP, cracking effort rises to 2.5" WC by the time IP drops to 100 psi. Attached to a Sherwood with a clogged filter that could be problematic. But balanced seconds are not similarly troubled.