Firstly you dont need your service tag, it only depends on your installed rom.
Secondly all it does is lead your to the download page to the pkgs,
all known available pkgs are available here
or on the update guide I linked to.
If you dont get a notification you wouldnt be able to update anyway, as it will check before install if you're compatable.
The currently available upgrade paths are
EU Wifi: 340/344 -> 507
EU 3g: 340/344 -> 507
US wifi: 340/344 -> 506
EU wifi submodel: 1A3
EU 3g submodel: 1A2
US wifi submodel: 1A3
The device string is constructed as:
xxxx is always LUN as this is it's codename (The dell codename for the s7 was "looking glass", the qisda codename was "luna")
yyy is the submodel number listed above
zzz is the current rom version
aa is the region.
bbb is not valid on the S7, but on the S5 and venue this is your modem region (either US, EU, or AWS)
So the upgrade paths are:
GLUNB1A334000 -> GLUNB1A350700
GLUNB1A334400 -> GLUNB1A350700
GLUNB1A234000 -> GLUNB1A250700
GLUNB1A234400 -> GLUNB1A250700
GLUNB1A334030 -> GLUNB1A350630
GLUNB1A334430 -> GLUNB1A350630
For the moment the US roms 325, 340 are not canidates to update, so they're either stuck on 2.2 or have to manually update.
Until the tmo update actually comes out I'm going under the assumption that it's not currently planned to come out.
(There is also the US 4G 322/333 -> 338, but it's very old)
This covers every publically available roms. Roms that are not publicly available will never recieve update notifications.
This system is identical to the one used on the Streak 5, 10 and venue
all the links do is link to the update pkgs and the update page. If you cant acces the update page to download them you wont be able to install them anyway.