No, you do not need to use that time format. That format is only really useful when it comes to displaying it to a human operator.

For your logger, you can simply keep your all times in seconds - and only convert to minutes, hours, etc for display.
This also has the advantage of being far more efficient in terms of storage.

This is the way that things like MS-Excel work - if you have Excel, look up "serial values" in the online help.