Can this ship ever operate without shore based air support?
Short answer is that of course it can. Slightly longer answer is that it will depend on the mission and how many cabs we eventually get.
Carrier capability does not necessarily equal replicating what the USN had in the eighties and nineties. They do not have the same capability now.
Carrier capability is defining the set of missions you want to do, projecting what that threat is likely to look like and building your airgroup around it.
Simple defensive AEW can be achieved with a helo solution, it just tends to mean that you
may need to allocate more cabs to DCA by adopting CAP vice deck alert. Where you do lose out is in the ability to control major strikes (the reason why FOAEW changed to MASC) and that is almost entirely speed / FL dependent. Of course an E2 solution would be better than a r/w solution, but that does not make the r/w solution useless, nor indeed the ship vulnerable. It's not as if the old Gannet plus APS20 did strike control either.
Last time I looked, the RN have rarely fielded an organic AAR solution other than Scimitar to support the Bucc S1 and Buccs with buddy tanks on the old Ark, principally for recovery serials. Was the Ark any less of a carrier capability?
For ASW, I can't recall an organic f/w ASW capability once Sea King HAS1 hit the decks in large numbers. Merlin HM2 is at least as capable and can be embarked on the QEC. Would I like a deeper field organic MPA? Hell yes, but we appear not to have had one since circa 1966, so adding one now will be one hell of an ask. COD is a slightly different issue, but actually what does a C2 really bring to the party that an RFA can't?
I think people are forgetting that we have never had a USN CVW capability and are comparing QEC (as a large and expensive ship) against it. This leads to some unflattering comparisons which do not necessarily reveal the whole truth. Some things need re-iterating :
1. QEC is not expensive because of it's size. It is expensive because MoD can't cost independently and because some non-RN senior officers have spent the best part of a decade suggesting that the ship was too big and therefore ought to be delayed or cancelled. This allowed the pollies to dither and this costs money - real money.
2. The ship will be big enough to operate a meaningful number of FJ and helicopters, which will allow it to play credibly in most scenarios - unlike the constrained animal that was CVS.
3. The ships will last fifty or so years. In that time we can buy more jets if required and even modify the ships to operate whatever comes after F35.
I think what I'm trying to say is that QEC will be a significantly more capable beast than CVS and quite possibly CdeG. Would we like E2D, COD, all the bells and whistles? Oh yes, but we can't afford them. What we can afford will actually be relatively more capable than any carrier we've had before and I include Eagle & Ark in that.
That is far from Conference league. Comparison with a CVN is the wrong comparison. It needs to be measured against the requirement it was designed against (circa 2000), which is still largely valid.