John,
No, the only grenadiers in the South with Cornwallis initially were the company of the Composite Brigade of Foot Guards, and that of the Queen's Rangers (both served with their parent unit). The 1st and 2nd Grenadier Battalions did take part in the siege of Charleston, but returned to NYC with Clinton. When Cornwallis took over command of Phillips' force in May 1781, he inherited the grenadiers of the 76th and 80th which (along with their light companies) had remained with the parent regiment.
In grouping the companies into battalions, generally it followed numerical precedence, with a battalion being formed of ten companies early in the war, but then getting larger – 14 or more was not uncommon. Occasionally, the CO would have his regiment's grenadier company transferred to his battalion (if it wasn't already in it), which could break the sequence.
Here are the orbats of the 1st and 2nd Grenadier Battalions during the siege of Boston, the brief stay at Halifax, and the Long Island/NYC campaign:-
1st Battalion (Lt Col Meadows [55th], Maj Mitchell [5th])
4th, 5th, 10th, 17th, 22nd, 23rd, 27th, 35th, 38th, 40th.
2nd Battalion (Lt Col Monckton [45th], Maj Stuart [43rd])
43d, 44th, 45th, 46th, 49th, 52nd, 55th, 63rd, 64th, 1/Marines, 2/Marines.
For the NYC campaign, a small 3rd Battalion was formed from the seven regiments that came up from the abortive attack on Charleston (15th, 28th, 33rd, 37th, 46th, 54th, 57th) and a similar-sized 4th Battalion from the double-strength companies of the Highland regiments (42nd, 1/71st and 2/71st). Both were disbanded in late 1776.
Prior to that, the single battalion at Lexington/Bunker Hill, was commanded by Lt Col Smith (10th) and then Lt Col Abercrombie (22nd):-
Lexington – 4th, 5th, 10th, 18th/65th*, 23rd, 38th, 43rd, 47th, 52nd, Marines, 59th.
[* combined company, about half-and-half]
Bunker Hill – 4th, 5th, 10th, 18th/65th, 23rd, 38th, 43rd, 47th, 52nd, 59th.
(The grenadiers of the 35th, 1/Marines, 2/Marines and 63rd were also present, but served in a small "flank" battalion of converged grenadier and light companies under Clinton; the 35th's grenadiers were parcelled out to the Royal Artillery as mattrosses.)
When basing your figures, if you want to consider seniority then the lowest numbered regiment went on the right, second lowest on the left, third lowest inside the lowest, fourth lowest inside the second lowest, and so on moving in towards the centre. So the Bunker Hill battalion would line up thus (assuming the enemy at the top of the page):-
5th, 18th/65th, 38th, 47th, 59th, 52nd, 43rd, 23rd, 10th, 4th.
The single grenadier battalion in the Saratoga campaign would line up thus:-
20th, 24th, 31st, 47th, 62nd, 53rd, 34th, 29th, 21st, 9th.
(it's possible the 9th and 20th swapped places, as the CO of the Battalion was from the 20th).
Hope that helps.