[Antennas] How important is the ground?

[Buck - N4PGW]

I have an IC-706 mkii that I operate as a base, mobile and portable.  When I
moved it from my car to my house last night, I followed my usual routine of
hooking up the antenna tuner, two-meter antenna, power and ground.  It
suddenly occurred to me that when I have been operating portable, I haven't
been using any kind of ground.

For portable operation, I have been using a dipole antenna fed with an
antenna tuner.  The radio is powered on the same marine battery I use at
home for a power supply.  At home, however, I have lots of RFI from
computers, appliances, etc. that give me an s-5 noise level if I don't
ground the rig.  Because of the noise level without the ground, I cannot
test to see if the ground makes a difference on the received or transmitted
signal or not.  

Would I be better off to carry along some form of ground rod for use when
portable?  I have been setting up on a picnic table and operating with no
consideration of ground since the dipole doesn't need one.

Thank you,
Buck
N4PGW