Sure you’ll notice a bit more sidewall bulge putting the 305/40R22 on your stock 9” wide wheels. Which may give you that extra “rim protection” from curbs you’re looking for. But more importantly IMO, is the 305/40R22 is an overall shorter tire than stock, by about 1/2”+. Which now means curbs pot holes and such that are not as tall will still pose a threat to damaging your wheels. Because now your rim is closer to the ground with the shorter tire and shorter sidewall height. Follow me?
1/2” doesn’t sound like much, but you’ll be able to notice it. It’s going to exaggerate your wheel well fender gap at stock height, and reduce your sidewall height which may make it ride a little rougher.
For what your trying to accomplish going to a 305/45R22 would be better. Wider and taller. However, there are trade-offs with that size too. With a taller sidewall you may feel the steering and handling response become sloppy or a bit “delayed”, maybe a bit more body lean in corners, etc.