DHCP by itself is a protocol that won't leave the local network. When a device does a DHCP discover it sends out a message to any host that's listening and says "Hey, I need an IP address please!". If there's a DHCP server there it'll reply and say "I've got an IP address you can have, it's x.x.x.x. Would you like it?" That's known as a DHCP offer. Next the client will send back a DHCP request message which says "Yes please, I would like that IP address!". After that the DHCP server will actually set aside that IP address for the client and pass the client all of the information it needs - subnet mask, gateway and so on. That's known as a DHCP ack.
Let's say you have 2 networks that connect together at a single router. Network 1 is 192.168.10.0/24 adn network 2 is 192.168.20.0/24. DHCP for network 1 is served by 192.168.10.1. Network 2 doesn't have a DHCP server so you decide to use the DHCP server in network 2. You need to configre a DHCP scope on 192.168.10.1 but even once you've done that none of the clients on network 2 will be getting an IP address as the DHCP requests won't leave the broadcast domain for network 2. If you then configure the router (or A. N Other device) to be a DHCP relay server then that device will itself listen for DHCP discover messages and will then relay them on to the DHCP server in network 1. The device will act as a go between between the DHCP server and the client in network 2 that's asking for an IP address.
When the process is complete if you check 'ifconfig /all' or similar on the client in network 2 it will list 192.168.10.1 as it's DHCP server rather than the device that's acting as a DHCP relay server.
There's reasons for and against using DHCP relay. In a previous life I used to run central DHCP for the European offices. The benefit was that when we made changes there was only 1 server to change. The big drawback is that a lack of connectivity anywhere in the chain could cause DHCP to be unavailable. Hardware failures can knacker you too, but with H/A and split scopes you can mitigate that to some extent. These days I wouldn't bother with it and just run local DHCP.
So that's a long winded way of saying no, it won't hep you access the router in that setup. If you explain a bit more about it (and maybe include a quick physical layout and IP addressing) we may be able to work something out for you.