Prepare to a folder to your USB. I don't know if it will work the same as a DVD but it will have the same files.
A DVD has a specific hierarchy that DVD players recognize. A computer will recognize the DVD format of a USB device if the user has their computer set up for that.
Also, most USB sticks are FAT32 formatted, therefore the maximum possible size for a single file on a FAT32 volume is 4 GiB minus 1 byte or 4,294,967,295 bytes.
That may not affect you now, but is very useful to know......
Most recent TVs will also play movies of common formats although I found with one you needed to alter the suffix of "m2ts" files to "mpg" before it would recognise them.
But TVs read the folders and files just like a computer. None to my knowledge will behave like a DVD player and show the menu so you can select movies from there. Instead you have to go to the folder and select the file to play.
We first assumed that you wanted to put a 'prepared' DVD on a USB drive, and there were several answers, one of them pointing out a limitation based upon the USB file system format. One thing that wasn't mentioned is that you could use DVDA's iso writer to create an iso image of the DVD, and store that on the USB drive. VLC Media Player will handle a DVD iso image file and display it on your PC as if you were playing a DVD. (including the disc menu structure)
Since you're wanting to plug into a HD television, it would seem that DVD Architect isn't the tool you want to use. I would just write the video files to an appropriate format for your TV directly from Vegas. Why bother with DVDA? That's an extra step!
I discovered my TV records USB movies according to the spec of the USB stick, which makes sense - if the stick is 'slow' it will record lower resolution than if the stick is 'fast'.
So that is possibly another factor to consider when loading the stick externally.... maybe make a test recording with TV, then examine file with MediaInfo.