The Crankbrothers tool is a solid choice for a tool to have with you on your rides. By MTBing sons carry it.
Will you need additional tools? It all depends on how much of your own bike maintenance you want to do. If you start doing more work you'll find the small folding bike tool to be too limiting and hard to use. For me, drivetrain maintenance is top priority. This requires a way clean and lubricate the chain. I use a chain scrubber and brushes for this with a good quality chain lube. I also have T-handle hex wrenches with a ball end for those tight and hard to reach fasteners. A torque wrecnch is a good idea as most tend to over tighten small fasteners and under tighten larger ones, etc, etc. After 20+ years of bike maintenance I've got a whole shop of tools...
As to carrying a 'compact inflator' for flats, I have to agree with
@Latitude , it won't get you very far. Some prefer calling AAA, or a friend/spouse. I do agree with
@Alaskan re a flat kit. I carry a flat fix it kit with a spare tube, tire levers, patch kit, tire boot, mini-pump, CO2 inflator, and cleanup wipes. Several of my favorite rides are out of cell range, so it's up to me to get my own *s* home! My usual practice is to swap tubes on the trail and use the CO2 inflator to get back to riding ASAP. I patch the tube back home and rotate it onto the flat kit as the next spare. I did have a blowout a few months ago that ruined the tube, no chance for a patch with the long split. Glad I had a spare!