Nope. But he could have taken on the name Joseph "unofficially" after being baptised.
My suggestions based on FHS CD and suggestions above, and all following in Nots St Mary:
Enoch G and Rachel were having children in the 1720-30 and this included Enoch(2) b 1729 and John 1736.
Enoch (2) m Mary Pemberton in 1759; their children included Enoch (3) (b1762).
John m Sarah Lacey in 1756; their children included Enoch (4) (b 1763); they also had a son John who himself had a son Enoch b 1785 and died 1792 (5)
I can't separate Enoch 3 and 4, and either Enoch 3 or 4 could have been the one who died in 1834 aged 70.
One of them married Sarah Smith in 1784 -- no mention of any Enochs born to them. Sarah died in 1800 and I suspect the same Enoch m Mary Hough 6/12 later - no children.
The other married Hannah Coates in 1788 and their children included Enoch b 1790 (6). Enoch 6 m Charlotte Mayfield in 1813; their children included Enoch b 1816 (7).
Burials include 1802 and 1807, neither named as "child of" so we can presume they were adult.
So - Enoch 2 (b 1729) could have been one of these maybe 1802.
Enoch 3 OR Enoch 4 died age 70 (ish) in 1834. The other died in 1807 (as Enoch and Hannah had children bapt up to 1805).
Enoch 5 b 1785 and d 1798
Enoch 6 b1790 - we haven't found a death
Enoch 7 could be the Radford Enoch as we know now there was a Radford link with the Stone family - died in the 1880s.
(One more Enoch was b 1788ish and died 1790 (?first child of Enoch and Hannah).
So though I can't separate them all out exactly, that would account for all burials and only leave Enoch b 1790 unaccounted for. And he's the one that allegedly died on the same day as either Enoch 3 or 4 - his father or uncle (although the date of burial for the older Enoch is not the same on the CD as given on the tree that started all this!!)
Phew, I think I've done my bit, off to do the washing up now!!