They very well could be, but dang does it make everything look different on the layout. It switched the entire colors from a cool grey to a warm grey which clashed with everything and completely flipped the mood for the client.
To fix this I ended up taking a screenshot of the design, converted it using Document Setup > sRGB > Convert, then just manually matched the hex of all my global swatches to the screenshot. Luckily the entire document was colored using these global swatches, or I'd be having to change the color of hundreds or thousands of pieces.
It'd have been nice to be able to do this sort of 'normalization' automatically, but I guess you have to get lucky and hope your monitor/os converts to sRGB in the same way Designer does.
Regardless, now my Designer doc is set to sRGB and the hex of the swtches/design/css/browser all match exactly, so it turned out alright. But I can only imagine the kind of pain someone would be in if they caught it a bit too late.