No, it does not. It reports the exact same address as B4A-Bridge. And just to be sure, I also installed
Network Analyzer (I just picked a network app with high ratings). That app agrees with B4A-Bridge. And then, to investigate an extra layer down, I also installed the wonderful
Termux and ran the command
ifconfig - which also agreed with B4A-Bridge for wlan0.
Buuuut then I also went into the Chromebook settings and took a look there, and that's where only one ip is displayed: 192.168.1.253. So, for some reason, it seems that the Android environment in the Chromebook don't see same ip as the chromebook. Perhaps some internal NAT going on?
I suppose this isn't really solvable, and it's not really important either. At least someone with this problem in the future can find this thread to get a better idea what's going on.
(The only remaining suggestion I have - barely worth implementing, I suppose - is in B4A-Bridge to show something like "You are running a Chromebook, this ip might not be correct - go check your network settings".)