The chassis produces different signals in a vector monitor as opposed to a raster monitor, so the answer would be a no, can't swap them out.
Ignoring the original request of swapping a larger tube in, that statement is incorrect on 2 parts. It's the yokes that are the primary difference between a vector and raster monitor (though of course the part of the chassis that drives deflection is of course different) but the RGB signals and high voltage anode driving the tube are going to be the same, and as such the tube is identical, with a minor caveot.
There are 5 parts to a monitor. The frame, the chassis (main electronics board), the neckboard (the electronic board on the back of the tube), the yoke (copper wires around the neck of the tube) and the tube itself.
In a vector monitor, only the chassis/neckboard and yoke differ. The tube is an identical tube to most other tubes.
However, that said, most vector monitors require a 100 degree tube instead of a 90 degree tube. The degrees are based on the angle the electron beam is deflected from the top to bottom of the screen, when looking at the tube in 4:3 layout, in other words as it exists inside a standard TV set, not a rotated "vertical" monitor.
A 90 degree tube means the tube is longer so the beams can't be deflected as much. A 100 degree tube is shorter, thus giving a larger angle of deflection. If you don't find a match you CAN use the wrong sized tube (in either vector or raster) but will have various geometric problems like bent lines around the edges of the tube.
Yes, you CAN find old TV sets, especially from right around 1980 that use 100 degree instead of the more common 90 degree tubes. It is usally very easy to spot. From the outside the TV will be shallower by an inch or so. Inside, the tube will be as well. In addition, 90 degree tubes usually have "19V90" etched (well rasied) in their glass on the back side of the tube in the black coated area. 100 degree tubes should have a different marking. Otherwise you can use the model number of the tube itself to determine if it is 100 or 90.
Of course, this assumes your existing tube is a 100 degree tube. I believe at least one vector monitor used 90 degree tubes. Post the model number from the sticker attached directly to your tube, and I can look it up for you. (Or look for the raised 19V lettering in the glass). The model number usually begins with 19VxxxP22 where xxx are various letters, or if it's a newer tube it may have a different number in centimeters like A63xxxxxP where 63 = 25" tube, 49 = 19" tube, etc..
Once you find a compatible tube, you MUST swap the yokes between the tubes. Unlike tube swaps in raster monitors that *may* be able to keep the TV set yoke attached and just use it (if it's electrically equivelent), a Vector monitor has a very unique yoke and must be moved from the bad tube to the donor tube. There are numerous web sites with information on that. Doing it for a vector is no different than swapping yokes on a raster monitor, the difference is only in the appearsance of the yoke.
Reading the original post however, no, you cannot replace a LARGER tube in an existing chassis. The voltages vary, and more significantly the amount of power it takes to "bend" the beam with the yoke varies significantly depending on the size of the tube (think about it.. a 5" TV can run on batteries because it only needs to bend the electron beam a total of at most 2" up and 2" down on the screen. On a 25" tube you can't run those on batteries because it must bend the beam about 9" up and down, requiring a different yoke and more power.
Some chassis allow use of 13 to 19 inch tubes without requiring component changes, but most chassis are required to work with a specific size (or small range) of tubes. E.g. 12-15", 19-21", 25-27".
And yes, I believe I saw a web page a while back that showed a Tempest undergoing a tube swap from an old TV set.