alpine registers a custom handler do_hup_signal to handle SIGTERM and SIGHUP (pico/osdep/signals.c). Its function seems to be sending COMP_GOTHUP to the composer to begin shutting down of the program.
For SIGINT sent by Ctrl+C, it seems that the code has to opt-in to process it by calling intr_handling_on and intr_handling_off (alpine/signal.c) around the time-consuming part. The code needs to check whether intr_pending is set, then do the clean-up works (including cancelling the progress spinner at the bottom by calling cancel_busy_cue).
Hence the "cancellability" of actions depend on whether the developer has implemented it.
These are from a quick look at the source code after having to wait a few times (so not sure if other trigger exists). I haven't attempted to locate the part for connecting to IMAP mailboxes.
BTW: A recent mirror of its repository on GitHub like https://github.com/petemoore/alpine might help when doing code searches.