Over 2 years, it doesn't really matter.
Some notebooks don't run with the battery removed, some do. Mine does, but I leave the battery in because it's effectively a UPS if the power goes down.
My favourite computer is a 6-year-old notebook. I did a third-party battery rebuild last year which cost about $200. As more and more notebooks are reaching EOL because battery packs aren't available, rebuild services are getting better and cheaper.