I guess so, but even if they retain a fighting force on paper, logistics tell the end.I have my doubts alt-Crusader could make it all the may to Tripoli, I think another operation will be needed in-between to finally secure Sirte.
The escape, the run, happened at the cost, if I read well, of most the equipment of the Italo German forces at Nofilia, not to mention that the following pursuit I suspect by the still fresh division will likely further exacerbate the losses and disorganization of the DAK. On the opposite side, even if exhausted and running thin on ammunition supply and air cover, the British Commonwealth forces remain coherent and can resupply faster.
The question is then, how much time will it take Rommel to recoup the losses and resupply? Or to be more specific, can he do so before the Allies close on Sirte, barely a hundred miles from Nofilia? Here, he would have the Ariete in support of course, but against the whole Allied forces, resupplied, higher on morale and better rested, while his forces are still somewhat in shambles, though I'm not much knowledgeable in the particulars of warfare, this doesn't look good an odd for holding onto Sirte.
Next question then, what's after Sirte at this point?