It says to add stress to an opponent until you reach 2 stress. Does that mean said opponent receives two stress right then and there?

Are you talking about the frequency jammer or whatever it's called?

The transport itself cannot have stress, the tokens are discarded as soon as it gets them.

The jammer's wording basically means that, if the target had less than 2 stress to begin with, it will receive stress until it has 2. The target is going to end up with 2 stress, but if it already had 1 stress then the jammer only adds one. The wording also makes it so that things that redirect the stress as it is received, such as that one shuttle pilot, don't work because the jammer's keep adding more stress until the target has 2 of them.