I dunno if a "full record" would show enough -- a driving record is really just a record of incidents/accidents and standing. Make sure when contacting the state department for driving records (in Cali, for me, it was the Cali DMV) they know the purpose of request, that a date of origin needs to be shown to verify driving experience for a license exchange for the province of Alberta. I believe, on their own, Alberta has access to your actual driving record, the states and provinces have an agreement in place to share that data. In some cases they might even be able to see the original date of first issuance (which they find relevant to understanding your driving experience), but even so, be prepared for them to formally request you get the record of origin.
When I was in Ontario (before moving to Alberta) and I went through this, I went through this process, and even though DriveTest could see the origin date, they formally requested me to get them the paperwork anyways from the state of California (the novice employee at DriveTest called it an abstract, which it wasn't). I initially contacted a California DMV employee who had just put through a records request. Thankfully after contacting them about the delay in processing, I got a hold of someone who actually knew the process of foreign exchange (this is the key part -- finding someone who knows what you need) and modified the request to include a record of origin and a driving record, in the case the latter was needed too.
Because of that, I had my license exchanged promptly (before moving to Alberta and exchanging Ontario G for Alberta Class 5), I'm sure it's the same for Alberta.
Be very adamant in getting what you need, depending on how lazy the state employee you talk to is, they might just try and push a simple driving record forward instead of what you actually need.