Can I run my MacBook Pro Late 2008 without battery forever? Is it bad in long term or anything? Does it make the system less stable?

Can I run my MacBook Pro Late 2008 without battery forever? Is it bad in long term or anything? Does it make the system less stable?

My battery got swollen (and I unfortunately noticed it very late and might have be running with it for months, which potentially explains all the crashes everyday and the trackpad not working anymore, the Apple test also says I have a bar of ram broken...) and I had to remove it because the back pannel did not close anymore... Can I still use my MBP normally forever that way? I was planning on buying a new mac anyway but maybe waiting for the next iMac upgrade in the year... Should I wait?