How many TUS surveys can be linked longitudinally?

I’ve used the individual linking variable CPSIDP to link the following TUS surveys, which seems consistent with the CPS 4-8-4 panel design:

Jan 1999 –> Jan 2000

May 1999 –> May 2000

Feb 2002 –> Feb 2003

May 2010 –> May 2011

Cross-checking the relevant demographic variables (sex, race, age) seems to give reasonable results. Am I correct in assuming that these are the same respondents? Is this a reasonable way to look at tobacco use data longitudinally?

Yes, as the Tobacco Use Sample Notes page states the longitudinal links you’ve noted are valid links. Also note, although official documentation does not state as such, it seems that the July 2014 and May 2015 TUS samples are also able to be linked longitudinally. See this User Forum question and answer by a user who stumbled across this possibility. As it sounds like you have done, after linking these individuals with CPSIDP and verifying the links are legitimate by checking demographic information, it is safe to assume these are the same respondents.