From a United perspective, his return may be perfectly timed. Everton will be hurting following a surprise loss to Crystal Palace, and Moyes will hope to exacerbate any festering dejection.
Defeat against Palace makes three points simply vital for Roberto Martinez's side, who sit one point behind the Gunners, in fifth place, with just four games to go.
Nine points further back, in seventh, Moyes will want a strong finish to the season to soothe over some first-year glitches.
The Toffees won this year's reverse fixture 1-0 and last season's home tie by the same scoreline.
Everton have no fresh injuries concerns ahead of Sunday's clash, as Martinez revealed during his pre-match press conference:
Elsewhere, Steven Pienaar remains absent, potentially in line to feature against Manchester City, while Phil Jagielka may be fit enough for a return to the bench.
He [McCarthy] is massively important to us and he should be fine. I was very pleased because we took a bit of a risk with him on Wednesday.
But he's fully fit, he came through okay and he's preparing well for Sunday. I don't expect that to be a problem.
Arouna Kone, Darron Gibson, Lacina Traore and Bryan Oviedo remain longer-term absentees.
With that team news considered, here's a look at Martinez's potential starting XI:
Fresh from signing a two-year contract extension, Tim Howard will start in goal, supported by an unchanged back four for the ninth successive game.
John Stones will continue to deputise for Jagielka, with Sylvain Distin, Leighton Baines and Seamus Coleman completing the unit.
McCarthy will resume his partnership with Gareth Barry in midfield, so sorely missed during Wednesday's defeat.
As ever, the three more attacking berths will provide Martinez with the most deliberation.
Steven Naismith and Leon Osman both made telling impacts off the bench against Palace, which seems likely to earn them a start.
Gerard Deulofeu, Kevin Mirallas, Aiden McGeady and Ross Barkley would then be fighting for the one remaining slot, which Mirallas may narrowly claim.
All three will support Romelu Lukaku, as he continues to lead the line.
With Wayne Rooney a doubt and Robin van Persie out, Stones and Distin will hope to keep Danny Welbeck quiet and limit United's entries into the final third.
Both defenders struggled at times against Palace and will want a more competent display with Jagielka nearing a return.
The England international was inspirational during this season's reverse tie, achieving statistical perfection in his tackles (4/4), ground duels (9/9), aerial duels (4/4) and clearances (14/14).
Stones and Distin will do well to cover his absence.
Elsewhere, Barry's performance was similarly pivotal at Old Trafford, completely winning the midfield battle and providing his side with the perfect platform to attack from.
He passed more (69) than any other player on the pitch—15 times more than any team-mate—created the most chances for his side and provided an effective shield in front of his defence.
His and McCarthy's exchanges with Michael Carrick and Co. will prove decisive to the final result.
Prediction: Everton 2-1 Manchester United
Statistics via WhoScored.com