Yes and no. A badly worn sprocket, especially a small one, transfers wear and elongation to the chain. The chain can then transfer this wear to the other sprockets if they get any significant amount of use.
So yeah, if you live in the 11t and rarely call upon other gears, then you can probably set back the clock with a new chain and 11t sprocket. But if you wear out the 11t and also use the other gears often, you'll trash them too (even if their tooth counts prevent the chain from skipping as readily).
I think I'm going to try 12T next to 11T (for e- and non-e). I'll show the tooth distribution of what I'm running now below this other comment from a different site:
IMHO Ebike cassettes should use different tooth spacing to non-ebike cassettes.
ie. 11,12,13,14,16,18,21,25,30,36,42
As you can see this would give closer jumps at the faster end of the cassette reducing wear.
I personally find anything lower than a 36x42 gear pointless unless my Ebike is switched off. (I realise this is not the case for everyone though)
I think 11, 12, 13 and 14 may be a bit overkill but I like the concept of 11, 12, 13...and then 15 or 16. Usually doing 100% steel Shimano 11-51T for the e-bike and 1-4 aluminum, 5-11 steel 11-52T for the other rear wheels; here is what a 12T insertion would look like for the Shimano 11-51:
11-(12)-13-15-18-21-24-28-33-39-45-51
Have to take out one other cog in the middle. After 15T it goes 3, 3, 4, 5, 6, 6, 6. That's tough!
24-33 (1.375) is 9, 21-28 is 7 (1.33), 18-24 is 6 (1.33), 15-21 is 5 (1.40). Very tough. Probably take out 24T and go ...18-21-28-33. A 5 to 7 jump and then only 3 for the 21 to 18. That's hard to do. Too jumpy.
If adding a 12 and 14T and then take out 24 and 33T: 11-12-13-14-15-18-21-28-39-45-51. That's 1, 1, 1, 1, 3, 3, 7, 9, 6, 6 (largest 3 cogs are riveted together). That may be better.