I'm running Mint with a setting that will 'suspend' after being idle for 30 minutes
If I create a cron job to run in the middle of the night (i.e. while its suspended) would it run?

And if not, what's the usual way to run cron jobs without leaving the machine fully powered up all the time?

No.Turn the machine on prior to the cronjob time.

In short, as implied above, you must allow the system to run in order for anything like eg cron to run.

Thanks very much for this.

For anyone else that looks at this question, I've found out about two possible approaches.
1. rtcwake : this can wake the machine up from its standby state. Having done so, a cron job can run as normal
2. anacron (or fcron) : Alternative cron that takes into account the fact that the machine might not be on all the time. Any jobs that have not run at the requested scheduled time are run when the machine is next turned on (after some configurable delay)

I'm going to explore using approach #1 and set an rtcwake time with a cron job and with a script in /etc/init.d