I was playing XCOM: Enemy Unknown on Classic Ironman and so I want to do for XCOM: Enemy Within. Since the Genemodded Armor looks stupid I want to completely neglect gene modding my soldiers. Will doing it without gene-mods make the game much more difficult?
It should be fairly doable.
Note that you're already setting yourself up for the second most difficult challenge level, so I make no guarantees of your ultimate success, but consciously foregoing all gene mods should mean you have a nice supply of Meld to build your MECH troopers' battlesuits with.
Just bear in mind that as long as EXALT is a going concern you'll be fighting people who /do/ have gene mods on a regular basis.
Short answer: yes
It can be done. My last few C/I playthroughs I barely used Meld (built one Mec) and only used Gene Mods after I had psionics. By that point, it was mostly "what could I spend money on now?"
Most of the Gene Mods are (to me) just gravy. Mimetic Skin was the only truly game-changing mod, and it's super-expensive now. Incidentally, you could gene-mod one soldier and have them be your dedicated operative, and very rarely see the armor.
Note: Money spent on equipment outlasts the soldier you intended to equip. Money (and Meld) spent on Gene Mods die with that soldier.
Final Answer: While Gene Mods can be quite helpful, and Mimetic Skin is pretty awesome, other paths can lead to success as well.