Would you agree if we called it 'modern calotype''
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Not really and here is why. A "calotype" is done using Talbot's method & formula for sensitizing the paper, etc. A "moden calotype", in my opinion, would be a calotype done with modern materials. The modern materials in this case would be watercolor papers with factory sizing (not necessarily gelatin based) and the raw chemical stock production having benefited from the industrial revolution and higher purity. Otherwise it is a calotype and all you would have done to make it "modern" is convert Talbot's grains into grams and drams into ml.
Using the Ilford MGIV to make the negative it is just a paper negative. Browse around over at (there was a url link here which no longer exists) (mostly pinhole cameras but lots and lots of examples made with B&W paper as the "film").
If you are wanting the calotype look then make a calotype but you won't get that somewhat painterly look from Ilford MGIV paper without some manipulation.
You might come close to the look if you try printing the RC paper negative as a salt-print on some toothy paper. Or a cyanotype and then do a bleach & stain to get the brown look. Although, technically, a calotype is the negative only, not the final positive. The positives made were probably salt-prints or maybe albumen (late in its reign, before the calotype fell to the wayside).
All that said, personally, I use graded RC paper for paper negatives (pinhole cameras) with some pre-flashing. Generally get bit more normal contrast and tonal range that way. But you can try sticking a #0 printing filter behind the lens/pinhole to control the MGIV paper a little bit. If you are using a lens, then a #8 yellow in front is fine but put a filter in front of a pinhole and you get to see how clean your filter is...