As far as I can tell, the answer is "no", or not without modifying the firmware.
Looks like Meshtastic is only for sending "Meshtastic messages". Thatcs disappointing
Discussion
Meshtastic messages are arbitrary text. Anything formatted as text can be sent. Signed or unsigned Psbt for example just require some copy paste work.
I get that, but I'm talking about: if I built a server app (or had a Nostr relay running) on one machine, and had a remote client machine that wanted to talk to it over HTTP (or send notes to the relay), that client can't just join the mesh and talk to the server over normal HTTP. I would have to push everything through the Meshtastic message protocol.
Common mesh networking soltions turn your router into a mesh node such that your entire LAN is on the mesh and machines just speak normal HTTP to each other (they just happen to route packets over the mesh "LAN" rather than through your ISP).
I mistakenly thought Meshtastic was a simple way to get that situation without fucking with routers. I seem to have been incorrect, unfortunately
Meshtastic is a keyboard to keyboard messaging app, useful but definitely limited.
Reticulum, which can use some of the same hardware or faster interfaces if available may suit your interests better.
Ah yea I've looked at Reticulum before; very cool.
It's a bit too specific, though, for my current interest. I think generic mesh networking approaches are more widely-useable (like what nycmesh does: https://www.nycmesh.net/faq#how) - for instance you could be running a nostr relay on a mesh network like theirs and other nostr users could be connecting to your relay through the mesh network rather than hopping out to an ISP. If the wider internet went down, the mesh would be uneffected.
I know that latter point is true for meshtastic as well, but given that you can't do anything with it aside from meshtastic-specific messages, it's quite limited.