Only if (a) people know you did it, and why; and
It can still be effective if they don't as I discuss here.
(b) you're not a one-shot time traveler, so that there is the potential for this kind of pre-punishment to happen again.
[Insert standard TDT argument about how by doing this, you're acausally increasing the number of other time traveling pre-punishers.]
However, your main point, that the effectiveness of this scales non-linearly with the number of punishers is correct. However, this appears to be more of an acausal co-ordination problem.
It can still be effective if they don't as I discuss here.
Your argument seems sound - basically, if criminals get enough apparently "random" misfortunes, people will eventually associate criminal = unlucky loser and be somewhat discouraged from that path, am I getting this right?
I would just note that "having a single time-traveler pre-punish one crime is worth some fraction of that utility" doesn't really seem to fit this system, since a single pre-punishment falls well under the 'random noise' threshold so its deterrence effect is ...
Here's an edited version of a puzzle from the book "Chuck Klosterman four" by Chuck Klosterman.
When should you punish someone for a crime they will commit in the future? Discuss.