This isn't something I have ever seen reported before, and it seems unlikely that you can see the message before it is sent, but then again to use the popular Photo sharing app Instagram as an example they start uploading the photo as soon as you take it, before you tag it or write your comments etc, then when you click upload it's already most of teh way there and they can just add the extra info. So it's not out of the bounds of possibility that iMessage works in a similar way to increase the perceived speed of delivery by essentially streaming it to the recipient who is then instructed to mask it with the dots until it received the all clear signal, as it were.
There's no real way for us to know this is happening, and all iMessage communication is encrypted too, so hard to find out with snooping etc. I would ask if the partial message you see before receiving the real thing is always the same as the actual text you receive, or if it ever changes, i.e. are you seeing genuine updates as they are type, or is the system tripping up and just flicking between showing your the message and the dots?