The one doesn't exclude the other; the imperial pretensions might become like the English claim on the French throne.
It's quite different : the english kingship legitimacy didn't depended from holding France. And even if you had a crisis at the end of HYW in England, it wasn't directly to the incapacity of Lancasters to hold the french kingship.
Carolingian kingship legitimacy, on the other hand, did depended from the king's capacity to maintain the imperial pretention effectivly.
It doesn't mean that it would result automatically into the fall of the king, but it would critically weaken its legitimacy and authority at the profit of principalities rulers, including in the succession.
Though following your reasoning, it might be might be safer for them to survive as duke of Lower Lorraine (Lotharingia) for a while.
Well, you do have
Charles of Lower Lorraine that did have pretentions on Western Francia. But being vassal of the emperor greatly weakened his position (the campaign of Lothar against Otto provoked some sort of national awakening).
You have as to take in account the Ottonian policy : hosting Carolingian rulers is a thing, allowing them to get on a throne and to resume a policy of expansion on their land is another (while Robertians didn't really pushed eastwards for centuries). Even if there's a possibility, the emperors may just shut it.
But assuming that Charles and his successors go the same way than Herbertiens (meaning that they would likely not be considered as "true" Carolingians but as "of Lorraine" dynasty), that proud themselves IOTL of their Carolingian ascendency, I don't see them being likely royal material, probably less than other dynasties actually : in fear of the return of their previous policies, and preference for more "national" lines (even if they adopt a different self-conception : it doesn't grant anything for how other consider them)
That said, I agree : it could still technically happen.