TL;DR version: Don't create vassals with ICC; Either territorial core ICC yourself or feed to a vassal, depending on your RCC vs. Annex Cost reduction and how you value 5 ADM vs 8 DIP. Waiting till high Adm Eff to core ICC reduces the penalty.
In other words, is there a way to diplo annex the Marwar provinces without the ICC? And does that ICC also apply to me coring it myself?
If the Marwar province is primary culture then the core will never expire.
To expand on this, at least prior to 1.23, you have to eliminate the ICC tag's core somehow to get rid of the extra cost. To do that, your options are:
- Province culture in different culture group as ICC Country: Feed to vassal, wait 50 years for core to expire before integrating OR use Revoke Core in a peace deal in a subsequent war.
- Province culture in same culture group as ICC Country: Feed to vassal, wait 150 years for core to expire before integrating. I'm not sure if you can use Revoke Core in this case.
- Province culture is same as ICC Country: The core will never expire (w/o changing province culture). In theory, you could feed to a vassal and hope they culture-convert the province then wait to integrate. This would probably take quite awhile (20-30 years for separatism decay, then the conversion) and I don't know if there are any vassal which will reliably culture-convert provinces, but presumably.
Frankly, the only method above I really find viable is Revoking Cores, but that's usually a pretty rare occurrence. It's usually better to just let ICC countries hang out (if you can) till you get high Adm. Eff. from Absolutism which reduces both the base cost and the impact from the ICC penalty. For example, prior to Adm. Eff, the coring cost per development would by 5 ADM * (1 + 0.5 ICC - RCC). With 50% AdmEff, it's reduced to 0.5 AdmEff * (5 ADM * (1 + 0.5 ICC-RCC) or 5 ADM * (0.5 + 0.25 ICC - 0.5(RCC)), effectively reducing the effects of the ICC by half. In other words, AdmEff "saves" you significantly more mana (= ICC%) when coring ICC provinces than when coring normal provinces.
As for feeding ICC to vassls vs. coring yourself, it depends on how you value DIP vs ADM. Integrating costs 8 DIP/dev while territorial cores cost 5 ADM/dev. Then you have to consider your RCC (normally -25% - 55% or even higher) vs. your Dip Annex reduction (-40% with Influence and Infl+Adm policy). e.g. for Ottos you'll have -45% RCC and -40% DipAnnex and with giving 5.25 ADM/ dev and 8.8 DIP/dev with +50% ICC. So that's a DIP/ADM ratio of 1.67. You have to ask, "is 1 ADM worth more than 1.67 DIP?" Maybe it is if you have a 3/5/3 and are filling out ADM ideas. Maybe not if you have a 6/3/4 and are filling DIP ideas and integrating other nations.