Yes, as friends. However; even in those days of furniture with skirts around them to conceal their legs, it would have been been anguish for Jo who seemed to have no sexual feelings for Laurie. She did NOT seem the type to be able to simply sit back and think of England (or wherever). Moreover, despite the fact that non-working class women were expected to marry and pin everything on their husbands providing for them, their children and possibly their financially distressed relatives (which Jo definitely had the latter), Jo resolved to defy that and insisted on sinking or swimming entirely on her own (and thankfully had her immediate family's backing). Also, she'd seen for herself how the promise of inherited monies had kept Laurie from truly striving for independence and how that had hampered his creativity so I don't think she'd have wanted to be a part of that.
Lastly, with Jo having nothing more than platonic feelings for him, Laurie would have grown very frustrated very quickly and likely taken it out on both of them had they gone through with a marriage.
Yes, Jo eventually wed Professor Bauer, but with the spelt out understanding that she'd ALWAYS be fiscally independent.
Also, in the end, Jo and Laurie DID resume their friendship and I think he respected her by maintaining her independence while he was happy to be married to Amy (who DID value riches and seemed to at least be able to learn to love him romantically enough to satisfy both of them).