Sorry this response took a bit. Short answer: It wouldn't do anything to interfere with it. Whether they should or not would depend on the math.
Levelshifts change combat level. Combat level determines, according to the wiki:
"A character's Combat Level determines their base health and the base strength of all their powers. It, along with the Combat Level of the character's enemies, affects their chances of hitting and getting hit."
Although I'm not quite certain it does on the HP part -- My brute had 2633 HP with or without her alpha slot.
The base strength of the powers modifies very, very little. In the case of going from 48 to 50 on my battle drones, the base damage change for Laser Burst is 37.65 (level 48) to 37.87 (level 50). We can assume the scaling is very similar from 50 to 53.
The biggest benefit that the minions get from the level shifting is the ability to hit their targets more often. With regards to the attack formula, players attacking critters of higher level suffer a larger accuracy penalty.
A 53 minion being attacked by a 49 player-minion (Level 48 + 1 for lieut) has a 39% BaseHitChance (player summon pets use player BaseHitChance, relative level +4). Assuming no to-hit and no defense on the target
HitChance = Clamp( AccMods × Clamp( BaseHitChance + ToHitMods – DefMods ) )
AccMods = the power's inherent Accuracy × (1.0 + the power's Accuracy Enhancements + all global Set Accuracy bonuses)
Assume no enhancements in the pet. The 39% for BaseHitChance is then multiplied by the 1.67x accuracy of Laser burst for a total for about a 65~% chance to hit. If the minion was level shifted to 53, BaseHitChance becomes 75%, and the total accuracy is 125.25%, clamped to 95%.
If we assume a level 50 ACC IO into one of the equip powers, it's a 42.4% ACC increase. You don't hit diminishing returns here, so we'll go ahead and divide this up like we did HP: 50%, 30%, 20%. Since this is a minion, they'd receive 50% of the ACC bonus, or 21.2%. AccMods now becomes 1.67 * (1 + .212) or 2.0207.
If the minion is 49: 39% base chance becomes 78%; a 13% increase over the previous math; which is pretty good (although not as much as putting an enhancement into the power itself). If the minion is level shifted to 53, the the accuracy is 151%... clamped down to 95%. No change.
If we use thugs instead, who have a 1.1 on their pistol, you're looking around:
49 = 42.9
53 = 82.5
49 + enhanced = 51.9%
53 + enhanced = 95% (99.99% clamped down).
I really should have used thugs instead of bots for the math the first time around (My mastermind is bots, so I checked there first).
The biggest thing to note is that this is with 0 ACC slotted into the pet power themselves. A full 6 slot of Sovereign Right provides 97.49% ACC, moving the numbers to something like
49 = 83~
53 = clamped
49 + enhanced = clamped
53 + enhanced = clamped
So as noted at the start, it wouldn't change much on the accuracy front, which is the biggest change for the level shift.