Is there any way to access a local server via a smartphone during developement, or must I test it online?
Yes, of course. If your smartphone can connect to your local network over wifi then it can connect to any device on that network (that accepts connections), including your server, just like any other computer can. I do this to keep tabs on mobile compatibility during development, but it is limited to the phones(s)/tablet(s) in your possession so it isn't a very thorough way to test.
If you are using a Mac, you can give a try to Sauce.
Sauce will provide you a virtual machine to test on every plateform a local/online website, which every browser. The free version is restricted to few plateform, but it can be enough for you.
Otherwise, you can configure acces your local server over your wifi. Just type the ip address in the url bar. But you will have to need all device.
If you just want to see how it renders in a responsive way, you can test it on the last Firefox release.