It probably would, as long as you have well-drained acidic sandy soil. Quite a risk it might become invasive, in the right conditions.
I find heather growing such a problem but seem to have found that lots of moisture and acid fertilizer help -- is this the right forum, by the way? I found that I had to use LARGE plants to plant or they dried out while immature, unless babied along with lots of watering. The soil puzzles me -- if sandy, and well-drained, one would need to water a lot [like Scotland's weather]. It's super dry in Victoria in the summer. Our condo landscaper said he'd heard that you could plant a new heather plant right on top of the central exposed stems of an old leggy one where it wasn't blooming [I didn't want to take out all the old stuff] -- so I experimented with this, put standard planting soil plus bagged compost from the nursery on top of the exposed stems, mixed with acid fertilizer, and planted the heather. They took! Got the required drainage, I suppose. Meanwhile I cut the old leggy one back a lot and it is doing much better, maybe partly the fertilizer. I fertilized a lot, with a lot of different fertilizers [this was not a well-controlled experiment], trying to mimic what I would think would be the sheep-fertilized heathers of Scotland... and it seems to be working. My big problem was I couldn't or didn't remember whether some are early winter heathers or summer heathers [now I think I've got it straight from observation] and forgot to prune [trim tops] at the right time... is a summer heather now putting some top growth out on the tips of the old browned blossom sprigs ok to shear now or because it's starting to develop buds should I leave it alone for this year? Will it re-develop buds if I did shear it now?
If no luck getting a confirmed answer here, you may want to try contacting the North American Heather Society, perhaps to ask if they have any members in Alaska you can communicate with. My gut feeling is that yes, some will grow there, but if you're not finding it at local nurseries, then perhaps not.
The Alaska resident might want to check out the Q&A at http://www.northamericanheathersoc.org/Site4/frame1.htm -- Pruning heather is discussed at workshops, in newsletters, etc., too. The various Chapters of the North American Heather Society and their executive members with all their contact information are listed. I now will have a source to go to for questions, and whether or not to do pruning on the summer heathers when it has been let go too [?] late and the new growth is starting at the tip of a spent flower stalk.
Probably there will be some native heathers somewhere near there, too, if the region is suitable. If the imports don't like it maybe you can play with these instead.
Re pruning summer heather "late" in early spring: [re various climates, my own question] One of the executive members replied to me regarding this, via email [see above Heather society] and indicated that yes, one can prune summer-bloomers now even though the new tips are coming on top of the older spent bloom from last fall... that some gardeners choose to do so to delay bloom for whatever reason... so I have trimmed off a combination of spent blooms and spent blooms with tiny new tips... therefore they may be a bit late. Will be an interesting experiment. Other summer/fall-bloomers did get pruned earlier, a different variety, and some are not yet showing any new tips...