Q:

Can と and な have the same meaning?

I was told that the following uses of と and な after 色々 were the same.

彼女のために色々と甘いものを買ってきた。I bought a bunch of sweets and brought them to my GF.
  彼女のために色々な甘いものを買ってきた。

If this is true, is this an added use of the generic particle と that is not listed in this definition?

と
particle / conjunction :
if;  when
このシャンプーを買うと素敵なヘアブラシがついてきます。This shampoo comes with a nice hair brush.
  彼女は、どうしてそんなことが可能なのかと尋ねている。She's asking how that's possible. ▾
and
１２と２４と７と１１の合計は５４です。The sum of 12, 24, 7 and 11 is 54.
  いまやろうと思ったのに。I was just about to get started any-how. ▾
with
私はあなたとお話してよかった。I have enjoyed talking to you.
  彼女は今忙しいので、あなたとお話できません。She is busy at present and can't speak to you. ▾
particle used for quoting (with speech, thoughts, etc.)
「美しい」とか「醜い」といった言葉は相対的な用語である。The words 'beautiful' and 'ugly' are relative terms.
  そういう相手の前では、私の見せ掛けだけの怜悧な技術は、見抜かれた時に負けていたと思う。I think that against somebody like that, my seemingly clever techniques would be seen through and then I would be defeated. ▾

How does the と in the first quote work?

A:

No, the 「と」 and 「な」 do not have the same meaning or function.  「と」 enables an adverbial function and 「な」, an adjectival one.
In the sentence:

[彼女]{かのじょ}のために[色々]{いろいろ}[と][甘]{あま}いものを[買]{か}ってきた。

「色々と」 modifies the verb 「買ってきた」.
But in the sentence:

彼女のために色々[な]甘いものを買ってきた。

「色々な」 modifies the noun 「（甘い）もの」.
Part of your confusion may arise from the fact that the first sentence is difficult to translate into natural English the way that it will show that 「色々と」 modifies  「買ってきた」.  
The second sentence would translate swimmingly into English --- "bought and brought a variety of sweet things".

