I do not have information that goes that far back, yet, and so am unable to confirm (or deny!) the information you have. I suspect you have seen the records on IGI (extracted rather than patron submission) that show John and Alice's marriage in Shepton Mallet in 1623 and her christening in Batcombe in 1607 (assuming these two Alice's are the same person).
I guess the graves, if existing, are very worn by now. One way to possibly get more information would be to look at the original parish registers which I would expect to be in the Somerset Record Office in Taunton. They may be difficult to read - from my experience clergyman of that date were not well educated and their writing was abominable!
I hope you manage to find something. Sorry I cannot help more. Rupert