It works with any computer with WiFi. BUT, the Marvell Avastar adapter within the tablet is a question mark since it does not like routers - and the mobile hotspot is technically a router (supports up to 4 devices and a range of about 150 feet).
You can contact Verizon customer support because it 'may' work with the Marvell adapter because Verizon is on cue to get the Surface 3 LTE model later this year. It too has the Marvell adapter as well.
I can tell you that there is no guarantee that anything works with these tablets (all models). WiFi has been the biggest issue there.
As an alternative and if you are in an area that has WiFi, you can get a USB WiFi adapter instead. I have one myself which is an off-brand and the crazy thing hooked right up with a Surface Pro 3. Since it is a different adapter, no worries of the Marvell
getting in the way (you do leave the Marvell adapter ON). Airplane mode shuts off both if needed. Those things are dirt cheap but can get pretty warm when in use.
A lot of airlines are now providing WiFi onboard now and you can try that as well when traveling.
The tablet itself cannot be upgraded for LTE and thus an external means is the only option you have. You can also wait and check with Verizon as to when they will get the Surface 3 LTE model and get one of those. It is Intel based and will run regular
software.