piggybacking a wireless router on a another router, and DHCP

At home, I've been using a Gigafast cable modem router to share our internet
connection amongst three PCs and a PlayStation.  Works great.

Due to my new employer giving me a laptop to travel with, I picked up a
Linksys DI-524 wireless router to take advantage of the wireless
connection.  I connected its WAN port to a LAN port on the Gigafast.  Quick
shot to the end result: Everything seemingly works fine.

However, in the process of setting all this up, the install wizard, not
surprisingly, did not have an option for "piggybacking" it to another
router.  It wanted me to power off the cable modem, attach the new router to
the cable modem and to the PC, blah, blah.  I called Linksys' tech support,
looking for finer direction, and was told that what I wanted to do was no
problem, just make sure to "disable DHCP on the Gigafast".  Well, in the
process of doing that, I "lost" my browser connection to the Gigafast
router, and I ended up doing a power cycle to get back to the factory
defaults.  At this point, the Linksys tech said that since they can't
support the Gigafast, I was on my own there, but that I should still disable
DHCP.  After hanging up with him, I connected the Linksys router, the two
routers "saw" each other, and all of my internet connections are working.

DHCP is still enabled on the Gigafast.  Is this supposed to be causing me a
problem?  Or is there a problem I'm not seeing?

TIA,
Dan