It is not only about getting the temperature of the base down, but also about some molecular processes going on in the base after pasteurization that take some time. This is why it is generally recommended to let an ice cream base ripen some time before churning it.
It is common to age mix for anywhere from 4 to 24 h. Crystallization
of the fat in the emulsified state occurs more slowly than when it is
in the bulk state (not emulsified). Fat crystallization rate depends
on the type of fat and emulsifier used (Adleman and Hartel 2001 ), but
generally requires up to 4 h for complete crystallization (Barfod et
al. 1991 ). [...] Further, there is considerable rearrangement of
molecules at the fat globule interface. The adsorption of proteins
that occurs during homogenization does not lead to the most
energetically favorable interface, particularly in the presence of low
molecular weight emulsifiers. At aging temperatures, the emulsifiers
displace protein at the fat globule interface (Gelin et al. 1994 ).
[...]
Freezing of improperly aged (“green”) mixes leads to ice cream
characteristics similar to those found with nonemulsified mixes.
Namely, there is less retention of shape and relatively fast meltdown
due to less than optimal destabilization of fat during freezing.
Goff, H. & Hartel, R. (2013). Ice cream: Seventh edition. (p.139) 10.1007/978-1-4614-6096-1.
I also have big doubts that the food processor method described in the linked recipe will lead you to good results. One of the most important keys to a well textured ice cream is to avoid the creation of ice crystals larger than 40 µm. Freezing the base to solid blocks and then stick it into a food processor won't get you even close to this scale. Even the most simpelst and cheapest ice cream makes using a pre-frozen bowl should yield better results.