They never try it, but they could have put the "After our heart attack do we actually die or is it a survivable heart attack and our consciousness is copied and sent back no matter what?" question to rest by having Pam present and awake at the time of Jeff's "death". She's around a full nine minutes after Jeff's heart attack, before her own - that should be enough time to get a "Sorry, he's gone" from a doctor or to see if Jeff's consciousness lives on in that time period.
In one replay, Pam herself was a doctor, so would be qualified to pronounce death.
On Jeff's fourth replay (after his Hedonism and meeting Pam replay), he appears in the summer of 1963, unable to bet on the high-stakes races he did before, and with the World Series months away, leaving him with money issues. So... even though he knew he was replaying he never paid attention to the 1963 baseball season at all? Given he was living large at the time, but he had his whole life to read up on that summer in case he decided to do something which would prevent him from placing those bets.