Does it work? Can I make potions that will frenzy, fear, and calm enemies as well at high levels as illusion spells with fully perked alchemy?

You can do invisibility potion, and paralysis, fear and frenzy poisons. But not calm.

It can but making certain potions in bulk is much harder than just casting a spell over and over. With illusion I can stay invisible virtually forever. By the time I need to use it again my magicka is already full. With potions I would need to keep up my stock and some of the ingredients take quite a bit of time to collect making it not as practical. But yes it is doable for the most part.

I actually do both cos Iike to make poisons, conjure a sword, poison my sword, turn invisible and kill people.
It works great!

It is true- you can make paralysis potions- but the spell version works against many more creatures that will auto resist any paralysis poison.

You can make invisibility potions- but you have a limited supply and so cannot use invisibility liberaly as if you could cast it at will.

Alchemy can stand in for these two items, but it is a poor-mans version.

That is not to say that alchemy should be disregarded in these areas- i would recommend carrying paralysis poisons and a couple invis potions on hand in case you do not have the magic on hand to cast, alchemy can backup and supplement the spells- or if you cant cast the spells, it can function as a lesser stand-in.

Consider that Illusion carries Quiet Casting, an effect you can't otherwise get. This is important if, say, you want to go around with a Bound Sword in stealth or feel like throwing a Fireball from the shadows.