Only if the helm still feels loose on your head. I take it you'll wear your coif as well so there may not be a need for a liner at all.
Let us know how the new arming cap + coif works as I like having options with my kit as well and I made my liner easily removable.
I can bring my arming cap and coif to MDRF next time if you want to try it; I'm hoping to armor up if I can get a few tweaks done and the weather cooperates so I will have them with me.
Leganoth, as Sir Brian said, whatever gets it "snug" is what you'll probably want to go with. You can attach padding directly to the helmet if necessary. The "blue cell camping mat" is/was available at Walmart/Outdoor shops and is about $10 for enough to do an entire set of armor with leftovers. It's not period, and it doesn't breathe well at all, but it's a cheap, stable option to start with.