As long as they are not lacy curtains, but plain voile, yes, that will keep carrot fly out.... I weight the edges with long planks of wood or scaffold poles, which seems to do the job
As for carrots and parsnips together, I think the reason that some say not to do this as they are both vulnerabe to carrot fly and carrot foliage smell attracts them to the detriment of the poor parsnips, which might otherwise escape attention
The net covering solves this problem very nicely!!