You can look here for stats on it:
For computers that support webgl 100% of them support 2048, hence that recommended limit. Looking at the graph you can use bigger textures but it won't work on all computers.
On a side note if you don't use webgl, eg turn webgl to off in the project settings you can have much larger images, but I couldn't find any info on the upper limits. The limits seem to be based on if there's enough video memory and if you run into graphics card limits, it just varies on how the canvas is implemented in the browser.