The short answer is yes.
If one end of a bracketed phrase inside a sentence starts with a dash, then it has to end with a dash, too, but if the phrase is at the start or end of a sentence, then use just one dash (or whatever bracketing symbol you're using—like these parentheses and this dash and comma, for instance).
But in that sentence, I'd use commas, not dashes. It'll read faster that way.
And yes, as mentioned above, use em dashes. If your keyboard doesn't make them, use two short dashes with no space between.
PS:
You're not having a sentence. You might be having a baby, an idea, lunch, or a brain cramp, but you're not having a sentence. You have a sentence.