Re: "Will an antique lathe this size work for a home shop ?" ... This is a "wide open" question. Whether the lathe works for your shop of not depends upon what type of jobs you want to do on it. Not knowing the condition of the lathe, it is impossible to make some kind of educated answer. If the lathe is intact, and everything on it works (or can be made to work correctly), the answer is a qualified "yes".
If you wanted to build parts for modern day robots or do fine gunsmithing, the lathe may be too loose, and not having collets makes work on smaller diameter (like 1/8" diameter to maybe 1/2") difficult. If you want to make basic machine shop projects or make an occasional bushing or turn down a shaft, the lathe is probably fine. Bear in mind the BIG advantage to a "screw cutting lathe" is just that: it is designed and built to cut threads without needing taps or dies, or on work where you could not use a tap or die. Sooner or later, you will probably want to cut screw threads on the lathe. You might need to make an arbor for something like a grinding wheel, or perhaps cut internal threads on some larger locking nut. Being able to cut screw threads is a major advantage. Old lathes cut screw threads just fine without benefit of quick change gears or thread chasing dials. As long as the half nuts work and you have change gears, you can cut screw threads. Just a bit slower than on a lathe with a chasing dial and quick change gears.
I'd suggest you look at the lathe as a learning experience. If you work on it to put into shape for regular lathe jobs, you will have learned about checking clearances in split bronze bearings, shimming to set the bearing clearance, adjusting gibs, and lots more. These are basic shop skills that are "building blocks" to a lot of other jobs you will encounter as you get into machine shop work. The Seneca Falls lathe is as simple as it gets, a classic little lathe. Great to learn about lathes, not just how to operate them. A lathe of this type is (forgive me for saying this), as "forgiving a machine as there is". A flat belt driven lathe will often slip the flat belt should you take too heavy a cut or "crash" the carriage into a chuck or faceplate while the lathe is running. IMO, this little Seneca Falls lathe is a great teacher and great first lathe if you are looking to learn from "square one", and not expecting a toolroom grade lathe.
With some patience and care, you could probably build model steam engines or some shop tooling on that lathe. Remember: in the nineteenth century, when that lathe was in production, people did lots of fine work on that lathe. It was all they had, and they were glad to get a lathe with screw cutting capabilty, and all the basic features generations of us have taken to be "standard" on lathes. I myself can attest to the fact that a worn lathe with a "swaybacked" bed can turn out fine work and hold some tight tolerances in the right hands. What one person turns up their nose at and calls "junk", an old time machinist will work with and get the jobs out. Working in jobbing machine shops years ago, I almost never saw a lathe that did NOT have a worn bed, loose cross feed nut so there was close to 0.100" backlash, and on it went. We started with lathes that were old when we got to them in HS, and in the shops of 45 + years ago, we worked with worn machine tools as a matter of course. If you use your head, eyes, and think the jobs through, an old worn lathe can do some amazing things. If you are up for learning and getting more of the "whoie picture" than simply learning to do basic lathe operations, this little Seneca Falls Lathe may be a good teacher.