Verizon now provides native LTE service in most of Alaska's population centers (Anchorage/the Valley/the Kenai Peninsula plus the Juneau and Fairbanks areas). The Verizon coverage map is accurate:
https://www.verizonwireless.com/feat...map=4glte#maps
Because it's a recent addition (previously, they roamed on ACS), they
only installed 4G LTE. If you have a 3G/CDMA device, it will not connect to native Verizon and will (slowly) roam on GCI's legacy CDMA network. As well, if you travel outside of the native LTE coverage area, you'll fall back to 3G/CDMA, but it will be roaming on GCI's legacy CDMA network.
Native T-Mobile subscribers may be able to roam on GCI (I cannot confirm, as I do not have T-Mo), but I can tell you that MVNOs that use the T-Mo network likely will not roam.
Among the national providers, AT&T provides the best coverage (by far) in Alaska, with Verizon in a distant second. T-Mo has no native service in Alaska (you'll have to rely on other reports about roaming agreements), and Sprint is the worst of the bunch (no native service and very poor roaming agreements, if any).
For mission-critical connectivity outside of the populated centers of the state, the only realistic option is GCI's newer GSM/HSPA/LTE network. They do have various prepaid products (SIMs, etc.) that may help.