If you don't want people to feel that this is expected then just tell them that you don't expect immediate responses.
By scheduling the message to send in the morning you are just setting the expectation to be awake and respond then, you aren't removing the issue you mentioned, you are just picking a different time to set the expectation.
There is an expectation that during core working hours people will be somewhat responsive. That will differ org to org, and perhaps in your org there are no set working hours. In that case my current approach probably doesn’t hold as much.
My experience has been that simply telling them not to feel obliged to respond doesn’t really cut it, and people feel obligated regardless. This may be a cultural thing too, and again will probably differ company to company and region to region.
By scheduling the message to send in the morning you are just setting the expectation to be awake and respond then, you aren't removing the issue you mentioned, you are just picking a different time to set the expectation.