Sure, that's possible. Let's this field is called "ID". You can add this code to your Submit button:
this.getField("ID").value = Number(this.getField("ID").value)+1;
Then just set the default value of this field to a different value in the copy you send to each person.
To do this the right way, you would need to have a server process that hands out the sequential numbers. See here for an example of how you can do this when everybody is using Adobe Acrobat: Getting a Serial Number Into a Form Using SOAP - KHKonsulting LLC
If you also have users who only have the free Reader, you would have to use FDF to get data from the server.
Hi, Thank you for the swift responses!!
I will try the KHKonsulting link and reply here if I have problem getting the code to work!