Yes this works, although, please be aware that 1920 x 1080 pixels will not provide you with a very good readability of text on a 24 inch screen. This resultion should not be used on anything beyond 20 inch.

I would recommend you therefore to pay a bit more and buy a 24 inch screen with 2560 x 1440 pixel resolution instead, it can also be rotated and text readabiliy would me much better, especially for smaller fonts. The scaling can be set in Windows or Mac OS, so that you will not have any issues reading text at all. If you set the scaling e.g. to 150%, you would have a 1920 x 1080 scaled resolution but with excellent text readability because there are a lot more pixels provided for the text rendering (no jagged edges around text).

AOC Q24P2Q (2560 x 1440 Pixels, 24 ")

Dell P2421DC (2560 x 1440 Pixels, 23.80 ")

BenQ BL2420PT (2560 x 1440 Pixels, 24 ")