Yes, definitely worth overhauling, if you plan to keep the bike. The grease in the bottom bracket is just as badly off as the grease in the hubs.

However, bottom brackets can sometimes be hard to remove, if corrosion has done its worst. If you run into stuck bits, stop and think, maybe come ask here, before getting frustrated or damaging something.

For example, on the bike I'm working on now, the fixed cup doesn't want to come out. I'm cleaning and regreasing it in place. On a previous bike this year, the adjustable cup wouldn't come out. Left that one in place and used thin shims under the fixed cup to adjust the bearing.

Not trying to dissuade you - most likely you'll have smooth sailing.