It's great to know what's going to show up on the finished product before you hit print. To give you a glimpse into that, QuickBooks Online has a Print or Preview feature that I recommend taking advantage of. This is typically available on the transaction window in the black bar that runs along the bottom.
It sounds with your question like you could be referring to the Memo section available for cheques on the transaction screen. If so, the answer is yes, that will print for your vendor to see.
If you mean something entered in the Notes section on the Supplier Information profile, that won't print. Data entered in that section of the supplier set up is for internal reference only and isn't something your vendor would see.
Check out this article to learn more about printing cheques: How to print cheques
Give me a shout if you have more questions! I'm here to help. :)
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