A *far* better solution is to add an ethernet port to your Amiga which is relatively easy to do on all models except the A500 and A1000.
For those two models, you can add a Z2 busboard sidecar, and then add a Z2 ethernet card. This is an expensive way to do it, but it works.
Once you have ethernet, then you can add an ethernet -> wifi adapter. Older adapters are dirt cheap on ebay these days. You really only need 802.11b for the older Amigas, since they'd only have a 10Mbit ethernet card anyway. I use an ethernet -> wifi adapter on my A4000 via an old Ariadne 2 card, and it works great.
RS232 is VERY cpu intensive on the internal chipset, not to mention dirt slow -- maxing out at 0.1Mbps.
