I would say no you aren't as you are a visitor and not a permenent resident, but AHC always seems to surprise me with some of their decisions. I would call and ask.
Are you eligible for AHCIP? Registration requirements
All eligible residents of Alberta must register themselves and their dependants with the Alberta Health Care Insurance Plan (AHCIP). If you are a new or returning Alberta resident, you must register for AHCIP coverage to receive insured hospital and physician services.
All eligible Alberta residents with appropriate documentation will be provided coverage.
Eligible residents
An eligible resident of Alberta is a person who is:
Legally entitled to be or to remain in Canada and makes his/her permanent home in Alberta;
Committed to being physically present in Alberta for at least 183 days in a 12 month period;
Not claiming residency or obtaining benefits under a claim of residency in another province, territory or country;
Any other person deemed by the regulations to be a resident not including a tourist, transient or visitor to Alberta.
NOTE: Individuals coming to Alberta on visas or permits from Citizenship and Immigration Canada may be eligible for AHCIP coverage, depending on the type of immigration document they have, the length of time on the document and their commitment to reside in Alberta for 12 consecutive months.
When you move to Alberta from another province or country, there may be a waiting period before you become eligible for coverage under the AHCIP.
Babies born in Alberta to a non-resident of Alberta are not considered residents of Alberta and are therefore not eligible for coverage with the Alberta Health Care Insurance Plan.