Do mutagens ever increase the "rate of evolution"?
Do mutagens ever increase the “rate of evolution”? [..] By "rate of evolution", I'm informally referring to either the amount of time or the number of generations that pass before some beneficial mutation occurs and is selected for


This is a very unusual definition of "rate of evolution" but I'm happy to consider it if you want.

If more mutations happen per generation, then it takes less time for a beneficial mutation to happen. So yes!

By rate of evolution, some people may like to refer to the rate at which neutral mutations fix (fixation=reaching a frequency of 1 in the population). If $\mu$ is the mutation rate, then $2N\mu$ mutations are produced each generation (assuming diploidy), and a fraction $\frac{1}{2N}$ of them fix (as they are neutral), this means that the rate of fixation is $\frac{2N\mu}{2N} = \mu$. So, again increasing the mutation rate increases the rate of fixation of neutral mutations. It is actually true also for deleterious and beneficial mutations but the computation is a little more complicated.

Note however, that there is a point after which the mutation rate is so high, that your population might be drawn to exctinction. This is called a mutational meltdown. Mutational meltdown is unlikely to happen unless the population size is already small to start with and/or the mutation rate is really really high.