Yes, you can specify fractional pixels. As this has been part of CSS since the very first version, it should be well supported by any browser that supports CSS at all.
"The format of a length value (denoted by <length> in this
specification) is a <number> (with or without a decimal point)
immediately followed by a unit identifier (e.g., px, em, etc.)."
When the elements are displayed on the screen, most browsers will naturally round the position to the nearest pixel when using 100% zoom level. On higher zoom levels you will notice that fractional pixel values are recognized.