You can totally use melee weapons on a magicka build, but you will have to recover magicka in other ways than heavy attacks.
I play my magicka templar with dual wield, and I recover magicka from class recovery methods, minor magicka steal, and one recovery glyph on my jewelry. I don't use it but you can totally get recovery from food as well.
Can go magic damage heavy increasing the chances of procing the magic damage status effect that comes with minor magicka steal, have a backbar resto staff for magicka recovering heavies, or use other mechanics like Warden's netch, vampire's health cost melee spammable, CP stars, DK's battle roar, Meditate, heavy attacking with the Psijic Order ability Mend Wounds, and other sustain mechanics. Sadly there are no melee weapons that restore magicka on heavy attacks, which isn't actually as bad as it sounds but I can see the appeal for one.
Nightblade siphoning strikes*** slotted + enchantment is how I play my Melee+Bow Magblade.
I'm sure they will make both weapon heavies restore both resources at some point OR you'll be forced to use a stave for magicka regen (I hope this isn't the case for majority other classes).