Does purchasing a (used) car with cash do anything to benefit ones credit score?

nope

This is not 100% sure, but this is what I would think.

Having assets is instantly good for your credit, so that is positive.

On the other hand, cash does not involve credit. I would think that the best thing for your credit would be to get the car using a loan or a credit card. Then pay off the principle of the balance more than what the actual cost per month is. This will reflect very positively on your credit statement. Use credit to pay it off on time or faster. That will reflect in your credit score.

No, Your credit report would not show the transaction. If you have the cash you can find a credit that if the balance is paid within a short amount of time interest will not be added and pay it off in that time limit then it will show up as a positive note and raise your score.

yeah... it will save you money in the long run allowing you to pay the rest of your bills on time so they will improve your score, but direct effect no it does not improve your score. seriously, always pay early and always pay $5 extra, keep creditcard ballances above $0 but below 50% of the limit with their highest ever between 80% and 90%... I just wish I had the income to follow this advice.

No, it doesn't because that transaction is not reported to the credit bureaus

It doesn't because you aren't making payments on it, so there is no credit built up. Credit goes a lot by your payments. If you pay bills on time, and in full amount all the time then you'll build your credit up. :)

It doesn't. I actually asked this once so I would know.