How essential is it to actually get the perks?

Say for example I wanted to get a good quality Ebony Bow. Obviously there's the option of levelling up smithing, spending the perks into Ebony Smithing and then making my own but what if I only levelled up smithing to say 100 but did NOT spend any perks in it and just went and found one at the bottom of a dungeon someplace?

Is there an advantage to having the actual Ebony Smithing perk itself in terms of quality when improving the bow? Or can I save myself the smithing perks to spend elsewhere and just level smithing to 100 without perks and improve it with that?

Only if you want to create the armor associated with the perks and upgrade it above normal levels.

Like the perk states: "and improve it twice as much". So upgrading with the perk makes it A LOT stronger.

When you have the related perks you improve items twice as much as you would without them. So yeah they're nice to have but you can do just fine without them too.