For sure. Overall, most plane shares are for higher performance models, though. This is knowledge the OP needs before they get too fired up about buying the 1/5 share of that Mooney they’ve just seen advertised. Also many (not all) groups of owners are leery about students.
Another issue is that if you want to complete all your CPL training in your own airplane it needs to be certified for intentional spins, which cuts down the list of suitable models by about 90%. If not, you’re going to have to go to an FTU for spin training, and the flight test (which includes a compulsory spin demonstration) will have to be split between 2 airplanes, leaving you with the problem of finding that second airplane.
So you’ll definitely save money by buying a share of the right plane rather than owning it outright, but it may take much longer to find a plane share (you're limited to what’s available at a local airport convenient to both you and your instructor) vs. buying one in toto which of course you can do anywhere across the country or even in the US if you want to put in the work, and then you can move that plane anywhere you need to. Another trade off.