Counterstamped Coins

As a general rule, yes. Some certain few counterstamps are known, and those tend to have a little collector value of their own, but that's rare.

Depends whether we're talking official counterstamps or not. Clearly coins with someone's initials on will generally have limited appeal. Counterstamps advertising a company do have some collector interest from specialists. And coins that have been stamped officially to show that they are acceptable for circulation can command very decent prices.

An example of the latter are the Spanish 8 Real pieces that were counterstamped by the Bank of England to pass as crowns. They were needed because of the shortage of silver in Britain during the reign of George III.