Possibly. And, it depends. Unfortunately, there’s no hard-fast rule that applies to every situation.
There’s not a 1-to-1 relationship between 2000 and 2010 counties, so you can’t just replace each 2000 FIPS code with a 2010 FIPS. Sometimes boundaries change. Sometimes new counties are created by carving out parts of older counties (e.g., Broomfield County, Colorado, in 2001). Some counties are eliminated and merged into their neighbor(s).
To deal with all these changes, you’d first need to decide whether you want your observation units to be the 2000 counties (e.g., with no Broomfield County) or the 2010 counties (including Broomfield County). If you choose 2010 counties, then you need to decide how you’ll “update” the 2000 data to match with 2010 counties. For example, in order to generate 2000 county data for Broomfield, you’d ideally allocate appropriate proportions from the 4 counties that Broomfield was carved out of.
For a simple approximation, you can use the population counts on the page I linked to. E.g., if 200 people lived in the part of Boulder County that became Broomfield, then you could allocate data from 2000 Boulder to 2010 Broomfield in proportion to that population count. (You’d also need to get the total populations for all these counties in order to compute the proportions.) But that’s still just a rough estimate.
The ideal way to generate 2000 data for 2010 counties is not to use 2000 county data at all. Rather, start from the smallest possible units in 2000 (e.g., blocks or block group parts) and allocate up to the 2010 county boundaries. That way, you’d be allocating directly from the part of Boulder County that became Broomfield, rather than just estimating that population.
This is all explained in more detail on the NHGIS Crosswalks page. Generating high-quality 2000 data for 2010 counties is exactly why we provide the crosswalk from 2000 BGPs to 2010 counties.
That said, if the data you’re working with isn’t available for any units smaller than counties, then you might have to follow the procedures I outlined above for allocating 2000 county data to 2010 counties. Or you can ignore some changes, or omit the counties involved in changes from your analysis… Like I said, there is no hard-fast rule!