You 'could' be right.
But, from my own database, I have an alternative.
There was another Thomas Quick lurking around Towednack.
Thomas Quick (probable son of Francis Quick and Elizabeth (Paule) was born sometime around 1646, probably at Towednack.
In Matthews 'History of St Ives ......' there is mention of a Rosewall deposition (c. 1680) in which Thomas Quick of Towednack, yeoman, age 34 is mentioned.
At some time probably around or soon before 1675 this Thomas married someone named Prudence and had four known children.
Zenobia (no baptism date) married Henry HICHENS at St Ives 12th August 1695 and she was buried at St Ives in 1746.
Prudence bp. 3rd October 1679 at Towednack married John NOALL at St Ives 24th November 1702.
THOMAS bp. 24th September 1683 at Towednack.
Martha bp. 18th July 1686 at St Ives.
BACK to Thomas and Mary.
As you have not mentioned it I would assume that you are not aware that Thomas and Mary had a daughter, Mary, baptised 26th December 1722 at St Ives (IGI).
Thomas Quick was buried at St Ives 3rd October 1724 and left a Will (of a kind) and, as it happens, I have a Transcript of this Will.
In fact, on reading what I have, it is the Inventory and Oblig. note.
The Inventory was signed by Robert Curnow, Samuel Noall and Richard Nichols and the Oblig. Note by Mary Quick, John Noall and Thomas Cubert.
Thomas' widow, Mary, also left a Will dated 4th September 1740 and proved 8th May 1741.
Mary bequeathed five shillings each to the four children of her Tenant John Row.
The rest, remainder and residue of her estate was left to her daughter Mary Quick.
Mary, the widow, was buried at St Ives in 1740 as 'Mary Quick, widow, of Bavella'.
Now, I also have a transcript of the Admon. and Oblig. documents relating to the estate of the daughter Mary Quick who was buried at St Ives in 1742 as 'Mary Quick of Bavella'.
I only need quote a small part of this:-
"The Condition of this Obligation is such that if the abovebounden
Zenobia Hitchens wid. &
Prudence ye wife of John
Noal abovebounden the
Aunts and Administratrixes of all and Singular the goods Chattells and credits of Mary Quick late of St. Ives ........."
I believe that should settle the identity of Thomas Quick.
Your idea was quite workable on the information available to you and I am not sure whether you were aware of the second Thomas Quick.
However, the additional data in possession of myself enabled clearer identification of Thomas.
Thomas, son of John and Jane, I believe will be 'Thomas Quicke ye youngest' who was buried at St Ives in 1701/2.
Now, back to work on some later Quicks at St Ives.