Blocking private IP space in this context means that the router has a rule along these lines
if (DST Subnet: 10.0.0.0/8 || 172.16.0.0/12 || 192.168.0.0/16 ) && (DST iface = WAN) drop
So, in other words, if the destination interface is the WAN port, and the destination subnet is RFC1918 space, drop the packet. Unless the 192.168.100.0/24 subnet exists on the LAN side, and is therefore in the routing table as something more specific than 0.0.0.0, the packets are going to be routed to the default gateway (eg. your upstream), and match the above rule and be dropped. If the subnet did exist on the LAN, then a route would exist, it would never match the default gateway and never end up going out the WAN to the cable modem.
Even something old but venerable like the WRT54G has this feature, and enabled by default.
Now, before your router has a public IP on its WAN interface, it is often possible to hit the 192.168.100.1 page from the LAN side - that's because in the interim while a public IP is being acquired, the WAN iface is given something in the 100.x subnet by the cable modem DHCP, and will have 100.1 as a gateway. But once it gets the lease for the actual public IP and real gateway, all of that gets dropped, and you're back to the situation described above
YMMV, but I've never been able to hit my cable modem status page with a default router config, on Comcast, in the decade+ I've had service with numerous routers from cheap throwaway no-names to WISP grade stuff like mikrotik and ubiquiti.