Is it possible to sneak to be sneaky with Heavy Armor?

oh yeah, definitely.

Ebony Mail (not armour, i mean the daedric one) has a good perk, and put Muffled on your boots. With a high enough level on sneak, you could even consider putting a point on the quieter armour perk.

I do it all the time, i'm a sneaky tank.

yeh just get the ebony mail

Sneaking success is based on the weight of your armor, light, and your sneaking skill.

So while it's possible, and completely valid, it'll be a little more difficult until you get the Conditioning Heavy Armor perk.