I assume from your description that water is also now entering the combustion chamber, and that does present some issues. Some of it will find it's way past the rings into the crankcase and you sure don't want coolant in the oil. Somewhat more remote is the possibility that you'll get enough water into the chamber to hydrolock the engine when turning it over and the result of that can be a rupture of the piston head. Changing a head gasket is at most a full day job for the novice, probably 3-4 hours for someone who has done it a few times. Were it mine, I'd fix it now, why take any chances? And change the oil when you're done and before you restart the car. Don't forget to check the cylinder nut torque after perhaps 30 minutes of running, again after a couple of hundred mines, and again at the end of the season.
If you've not done the job before, here's a primer which might be useful reading.
http://www.packardclub.org/forum/viewtopic.php?f=14&t=863This Post was from: https://packardinfo.com/xoops/html/modules/newbb/viewtopic.php?post_id=161533