I believe so. If I recall, the guides I had seen prior to making mine often went down that route, but it was something that was only useful for Workbench 2.0 and above. There's no TCP/IP stack that will run under kickstart 1.3 or below, as far as I'm aware. You might have to mess with settings on the terminal you're using to best interact with the TCP/IP stack.
That's all quite a lot of junk running just to get on the BBS' though. If you're also wanting to browse the World Wide Web, which is why I imagine you're asking the question, then I guess getting it all to work in a single configuration is your goal. And yes, I'm fairly sure that setup would work on kickstart 2.0 and above machines, though I can't currently offer any insights into getting that setup to work. I'm almost positive there are guides out there showing off that setup, though, of course getting them to explore the BBS' on that setup, not sure I've ever seen them dive into that. For most people it seems to be about the "oh look! Isn't this cool?! I'm on google with an Amiga!"
I've recently setup my WB 1.3 500 to use a software kickstart switcher, which boots perfectly into 2.0, 3.1, heck, even 1.4 and 1.2, with practcily no down side. It partitiions a section of my A501 RAM expansion as the kickstart, remapping everything to that. So while using kickstart 2.0, my normally 8mb A501 registers as 7.5 mb, because that half meg is using kickstart 2.0, or whatever I choose. At the moment it's only really useful with 2.0, because I also have Workbench 2.04 on my DH1: partition, which I can tell it to boot to when starting up the 2.0 ROM.
Anyway; There could very well be a future project where I go down the TCP/IP stacks in an attempt to browse the World Wide Web on my 500, and if I figure that process out, I will be sure to also show off the BBS', because that's the true fun of getting your Amiga online, if you ask me.