Does SERIAL capture the order of enumeration?

I’m working with full count historical census files (1900-1940), and am trying to establish the order in which households were enumerated.

For smaller samples, the combination of LINE, PAGENO, REEL, and MICROSEQ gives the order of enumeration, but they aren’t available for the full census count. Can I use SERIAL for the same purpose? I.e. do sequential SERIAL values indicate that households were sequentially enumerated?