The う in なかろうと is an auxiliary verb ([助動詞]{じょ・どう・し}) and as chocoさん says in comment, the と is a conjunctive particle ([接続助詞]{せつ・ぞく・じょ・し}). The combination of 助動詞「う」 and 接続助詞「と」 expresses that the statement is hypothetical, and the following statement (which is 「そんなものは何の意味も持ちえない」 in this case) contrasts with the former statement which includes うと.
The link in chocoさん's comment is the definitions of [助詞]{じょ・し}「と」. The forth definition in the second section is the one which explains the meaning of this kind of うと. The definition is already cited in chocoさん's comment below this answer, but it's important, so I bring it up here gratefully.
4.[逆接]{ぎゃく・せつ}の[仮定]{か・てい}[条件]{じょう・けん}を[表]{あらわ}す。たとえ…であっても。…ても。
㋐ [意志]{い・し}・[推量]{すい・りょう}の[助動詞]{じょ・どう・し}「う」「よう」「まい」などに[付]{つ}く。
[覚]{おぼ}える is a verb. It's not 覚 + える. If the word [得]{え}る is added to 覚える in order to mean can, able, or possible, it would become 覚え得る which is read おぼえうる. Instead of [覚]{おぼ}え[得]{う}る, 「[覚]{おぼ}えられる」 is commonly used these days, though.
The listing below is the grammatical composition of the phrase 覚えてなかろうと.
[覚]{おぼ}え:Verb ([動詞]{どう・し})「[覚]{おぼ}える」 in the Continuative form ([連用形]{れん・よう・けい})
て:Conjunctive particle ([接続助詞]{せつ・ぞく・じょ・し})
なかろ:Subsidiary adjective ([補助形容詞]{ほ・じょ・けい・よう・し})「ない」 in the Irrealis form ([未然形]{み・ぜん・けい})
う:Auxiliary verb ([助動詞]{じょ・どう・し}) in the Terminal form ([終止形]{しゅう・し・けい})
と:Conjunctive particle ([接続助詞]{せつ・ぞく・じょ・し})
So, the うと makes [覚]{おぼ}えてない hypothetical, which means, the fan-translation "What I remember" is not accurate, and your translation "Even if I do not remember" correctly expresses the literal meaning of 覚えてなかろうと and the contrast nuance it implies.
覚えてなかろうと is equivalent to 覚えてなくても in meaning, although 覚えてなかろうと sounds a bit more dramatic than 覚えてなくても.