It’s going to depend on everything is configured. I would expect good results having the Xbox configured for 480p and widescreen disabled; and the OSSC set to pass-through 480p and line2x 480i (these are defaults). If your monitor supports 960p, you should be able to swing line4x on 480i and line2x on 480p, but test with the smaller dimensions first.
If you’ve got the Xbox set to allow widescreen, it’ll output anamorphic widescreen in compatible games/menus, which is still a 4:3 frame (and the OSSC doesn’t read the aspect ratio metadata from the Xbox’s component output, so it has no idea it’s not 4:3), so that’ll give you that horizontal squishing in those instances.
Depending on the input you’re using on the OSSC, you might also end up with some weirdness with DTV 480p enabled (defaulted on for AV1, AV2; defaulted off for AV3), which makes the OSSC increase the sample rate, giving you 720×480 output (Typical dimensions of consumer-grade SD/ED content); changing ‘480p in sampler’ from ‘Auto’ to ‘VESA 640×480@60’ might give you a wider image at the expense of a slightly incorrect aspect ratio (which you should be able to adjust using the monitor’s image adjustments) or slight clipping of the left and right sides.