Absolutely. Criminal history is a valid and lawful criteria of discrimination. The tolerance varies by industry. For example the finance industry will have 0 tolerance.
It depends on the state. Some have "ban the box" laws that prohibit asking about convictions until a conditional job offer has been extended. Given that (unexpunged) convictions are public record though, it's pretty easy for them to find out if they bother to run a check and decide another candidate is a better fit.
To add on one anecdotal data point, I've never worked anywhere that didn't do a criminal background check. If you have a public record expect that everyone you work with knows.