Cannot speak for randoms, only the Solo Aspect: You can take control of any additional party members (also works in Multiplayer) so playing alone is technically definitely possible. What I can tell you from my brief experience though is that managing the extra characters is somewhat tedious so I don't think you'll get the maximum out of the party solo. Playing with only one character is not really something I'd do, there does not seem to be any mechanic balancing out all of the disadvantages there from what I can tell.