Theoretically yes but the IAC-2 will NEVER carry Mig-29Ks as it will be CATOBAR configured as stated and Mig-29Ks can't operate from such a configuration.
If indeed the DND at NHQ has frozen the design of IAC-2 as a CATOBAR carrier then it means that CAT tech is forthcoming from the USA, though the IN will keep pitching for E-MALs. That will be a political decision between GOTUS and GoI. Lets see.
About the aircraft on the Carrier, the MiG-29s can be modified for Carrier CAT operations, it is technically possible. But logically Rafale-M may be a more appropriate choice. Then there is the LCA-M if it gets suitably executed. The F/A-18 is an outside choice, unless it gets tied into some package with E-MALS!
On a Carrier of the size that is being talked about, it is possible (even advisable) to have more than one kind of fixed-wing jet; depending on mission requirements. So we are likely to see that happen.
The other matter is that the talks with USA for the E-2D Hawkeye now dove-tails nicely with the idea of a CATOBAR Carrier of this size. So that is a distinct possibility. Somehow the IN's interest in the V-22 Osprey never progressed beyond the preliminary, and if a CATOBAR configuration is decided on then the Osprey will go out of mind.
Most importantly, the IN aviators have always been proponents of CATOBAR operations right from inception. When the Sea Hawks were due for retirement, the IN actively pursued A-4 Skyhawks which could have operated from the old INS Vikrant. For some time, the US even seriously considered it, then went cold. Then IN looked towards the French for the Etendards, but to operate them; the Vikrant's tired old CAT would have to be replaced. Politics of that time ruled out that as well as eventually the Etendard. So the IN then looked at the Sea Harriers. Now the Fleet Air Arm will come full circle to what they learnt to do first. And will even look to buy the Goshawk to train rookie pilots.
After IAC-2, what next? Will there another generation of an even larger Carrier to be built in India? Any views?