I don't think an Intel NUC portends anything from Apple. When the Skylake chips were announced, it was pretty obvious that they could be used in a NUC form factor so the Intel NUC announcement, vs. the Skylake chip announcement, is no big shakes.
I think what will portend what could come in a Mini is what comes in the MBP and that may come in a few days. I don't think the Mini will be announced on the 21st, but if somebody has insider knowledge and it is announced, it will be a pleasant surprise, even though I'm not an imminent buyer. History argues against a March Mini intro. Only 2 of the 9 Mini intros happened in the first quarter, and in both cases, there was another Mini intro later in the year. I'm sure that Apple planned dual intros in those years and thus had to have an intro earlier in the year.
The prices I mention below are the Intel "list" prices. Who knows what Apple actually pays but I give them so that one can get some idea of what would be realistic from Apple's financial standpoint. Also, all the chips mentioned are mobile chips.
The i7 3.0Ghz dual-core in the 2014 Mini is the i7-4578U and it's list price is $426. By contrast, the i7-6770HQ, which is a Skylake 2.6Ghz quad-core with Iris Pro 580, is $434. (Yes, the dual-core i7 looks like a ripoff at list price.)
The i5-4278U 2.6Ghz dual-core in the 2014 Mini is $315. The Skylake i5-6350HQ is a 2.3Ghz quad-core, but no hyper-threading (so it can support the same number of threads as the dual-core i5 Minis), with Iris Pro 580, is $306. If Apple wants a cheaper chip, it can use the i5-6440HQ 2.6Ghz, also a quad-core, no HT, but with the HD 530 GPU at $250.
The i5-4260U 1.4Ghz dual-core in the 2014 Mini is $315 (there must be a big discount on that price). The Skylake i5-6300HQ 2.3Ghz is quad-core, no HT with the HD 530 GPU and it costs $250.
The reason why I list the i5 non-HT quad-cores is that all of the Skylake processors I listed use the same socket so one logic board should be able to be used for the different processors. That's not possible if one used the Skylake i5 dual-cores and the i7 quad-cores. I think reducing manufacturing complexity is important for Apple.
With these processors, I think it would be realistic to charge $599 (6300HQ), $799 (6350HQ) and $999 (6770HQ), which I think is what they did for the 2012 Minis (get rid of that 2014 1.4Ghz model). And unlike the 2012 Mini and especially the 2014 Mini, I think people would find the high-end more attractive than the mid model.
The Thunderbolt 3 + USB 3.1 chip from Intel lists for $8.55 for the dual-channel model. It's also being used in laptops so it should be able to be used in a mobile-chip environment.
So I think to get a quad-core Iris Pro 850 with Thunderbolt 3 + USB 3.1 is certainly realistic within the financial constraints of what Apple is looking at. The big question, of course, is whether other considerations play a bigger factor (cannibalization of more expensive Macs, lack of interest in the NUC-sized market, etc.).
EDIT: While the Iris Pro 580 is nice, it should be noted that it doesn't officially support 5K monitors and can only drive HDMI 4K monitors at 30Hz (DP is at 60Hz).