No you can't but for the database I'd choose something like AWS RDS for stability.
We've been doing this with Heroku anyway. Something about Heroku Postgres seemed a bit temperamental with our app (and was more expensive) so we've been using RDS in the same region without any complaints while enjoying Heroku for deployment.
Does RDS require a lot of maintenance and management?
No one on our team has DevOps or DBA experience -- we feel good about Heroku PG (even as inflated prices).
So far, not really. You need some basic AWS experience for security/scaling/setting up alerts purposes, but beyond that the only "ops" I've done in two years has been manually triggering some upgrades (paranoia on my part) and we ran out of disk space at one point as I forgot to set up an alert but this was very easily fixed.