Yes, this is possible and will not cause problems as long as it's configured properly. To setup the second DHCP server as a "failover" you will want to divide up the scopes DHCP 1 is serving. To do this you would configure the same scopes on DHCP 2 as there are on DHCP 1. You would then exclude a percentage of the scope on DHCP 1 and then exclude the opposite percentage of the scope on DHCP 2. This way together they would be serving the full scope.
Microsoft recommends using an 80% / 20% divide but there is debate on what works best.
Make sure that if you have any reservations set that they are setup on the secondary DHCP server (if they fall within the scope that will be served from that server).
DHCP 1 DHCP 2
scope 192.168.1.0/24 192.168.1.0/24
exclude 192.168.205 - 254 192.168.1.1 - 204