Help & troubleshooting for channels on your Roku device, including adding/removing channels, logging in to, authenticating, or activating a channel, channel-specific playback issues, assistance contacting channel publishers to report issues, and adjusting channel-specific settings.
I see that nobody that actually knows the answer has responded so I'll venture a guess.
I think it is unlikely the Spectrum app will work unless you're connected to the internet through a working Spectrum account. If Spectrum allows an already-installed copy of its app to continue to work when away from home on a non-Specrum account, I'd expect it to require you to authenticate it with credentials for an active Spectrum account.
Roku Streaming Stick +, 3810X, Ser YH0059427035, wifi LivRm - Samsung UN55ES6100
Roku Streaming Stick, 3600X, Ser 5S56D8240827, wifi BedRm - JVC EM37T
Roku 3, 4200X, Ser 4124C7087583, wifi GstRm - Sanyo DP26640