If a Korean could help with this, I would really be appreciative, because I'm kind of confused. But this is the way I understand it.
~면서 means while. It can be used in 2 forms: ~하면서 or ~한다면서.
It's helpful for me to think of the other suffixes in parts.
할지도 모른다면서:
Maybe you know the phrase 할지 몰라, which means, "(I) don't know (what) (to) do."
~도 can be understood to mean 'even' in most cases, but in this situation, it doesn't really change the meaning of the sentence. 할지도 모르다 is almost the same as 할지 모르다. Both of these statements are saying something like, "I'm not absolutely positive, BUT..."
In English, in most situations, we might say something like 'probably' or 'might'.
For example: "그는 마약을 할지도 몰라요" = "He's probably doing drugs." or "He might be taking drugs."
Although this is kind of hard to translate, and have it still sound normal, "할지도 모른다면서" is something like "while not knowing".
가보라더라고:
가보라 is 가보다 in the form of a command.
~더라 is similar to "I've found that..." or "I've heard that..." or "People say that..."
~더라고 is used to show more emphasis [I THINK...not 100% sure about that, but I'm pretty sure '고' does not change the meaning of the sentence]
쓸데 없는 소리:
쓸데 없는 말/이야기/소리 is very similar to what you were thinking: Nonsense/Talking for no reason/Talking just to talk/Useless Words
So in English, I think of the sentence saying something like, "While not even knowing if 혜미 would say a bunch of foolishness, 민희 told me to go (or to come here)."
But I asked my one of my Korean friends about it, and they told me it means:
혜미가 쓸데없는 소리를 할지 모르니까 가보라고 했어.
...which is really different from what I was thinking.
This says, "BECAUSE (I?) don't know if 혜미 will say nonsense, 민희 told me to go."
PLEASE HELP ME UNDERSTAND THE GRAMMAR =(