Nope, multiple resets, turning the phone off and then on after some time, going into airplane mode and then coming out of it, disabling Wi-Fi, disabling LTE, etc., none of that would get it going.
Generally the error would be not able to contact update server and to try again essentially, except it would be like that for days, so it's not related to servers being overloaded or anything like that. And it doesn't seem to be device/carrier related as people would often post the same device and carrier combinations in various threads mentioning they are downloading the update OTA or recently updated OTA without issues.
My phone over the past few weeks would have the "Unable to Check for Update" error instead of showing my phone was up to date. However, after Beta 4 was released this afternoon, it updated as it should and no issues.
my phone showed the same error when I tried to go from beta 2 to 3, finally did a manual update, after beta3 it showed software is up to date, and now shows unable to check for update again.