It doesn't matter if the other person is busy or not you can always send someone an email.
You can always send someone an email regardless of whether they are busy or not.
1) It doesn't matter if the other person is busy or not you can always send someone an email.
「相手が忙しいかどうかに関係なく、いつでもメールを送れるのは便利だ。」
it doesn't matter で「関係ない・構わない」
2) You can always send someone an email regardless of whether they are busy or not.
「相手が忙しいかどうかにかかわらず、いつでもメールを送れるのは便利だ。」
regardless of ~ で「〜にかかわらず」
「相手の都合」は
if the other person is busy or not
whether they are busy or not
としました。
ご参考になれば幸いです！
日本 
