Only way to check is to contact the supplier directly and verify or have the H110 mobo be provided with an updated BIOS (using a 6th-gen CPU) as a request, if possible, so that your 7th-gen CPU would work.
If by chance the mobo doesn't, you need to buy a 6th-gen CPU so you can update the BIOS yourself (before using the 7th-gen CPU).
If it does have an updated BIOS already, then, that i3-7100 will run/boot up your Asrock H110M mobo out-of-the-box.
Note also that the H110 mobos only run the RAM in 2133MHz speeds (unlike the B250 and H270 mobos I suggested). So, since in your parts list, you will be using 2400MHz RAM, it would only run in a downgraded 2133MHz speed.
Alternatively, to save on costs, you can consider getting the 7th-gen Pentium G4560 instead of the i3-7100. The G4560 does have 2-core but is one of the few Pentiums that HAS hyperthreading (4 threads) which is similar to the i3-7100 (also with 2-core/4-thread) but runs at a slighlty higher clock speed (+400MHz). Their difference is only about ~10% in performance (http://cpu.userbenchmark.com/Compare/Intel-Pentium-G4560-vs-Intel-Core-i3-7100/3892vs3891) but you can save $20 for a better and appropriate motherboard.
The Pentium G4560 pairs nicely with the GTX 1050 Ti (and, to an extent, even a GTX 1060).
The cost of your i3-7100 + Asrock H110M-ITX/ac is at $178.88.
The cost of the G4560 + MSI H270I Gaming Pro AC (if you really need wi-fi connectivity) is $173.67:
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel - Pentium G4560 3.5GHz Dual-Core Processor ($89.79 @ OutletPC)
Motherboard: MSI - H270I GAMING PRO AC Mini ITX LGA1151 Motherboard ($83.88 @ OutletPC)
Total: $173.67
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-09-18 14:37 EDT-0400
If you don't need wi-fi, and wired/ethernet connectivity is enough for your rig, you can get the G4560 + MSI B250I Pro for only $161.77 (after a $10 rebate in Newegg):
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel - Pentium G4560 3.5GHz Dual-Core Processor ($89.79 @ OutletPC)
Motherboard: MSI - B250I PRO Mini ITX LGA1151 Motherboard ($71.98 @ Newegg)
Total: $161.77
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-09-18 14:39 EDT-0400
If you really really want that i3-7100 at $109.89, and pair that with any of the above suggested 7th-gen motherboards, the H270I costing $83.88 or the B250I costing $71.98, it will only cost you a total of either $193.77 or $181.87, respectively (the first being $14.89 more and the second being just $2.99 more -- all for which don't need a BIOS update and will run your 2400MHz RAM at its rated speed).