I don't have any definite evidence but I think it's rather unlikely the filter would be as 'efficient' presuming you mean if you filter only allowing the same frequencies you'll get the same lumen output. The primary reason why you see lower lumen output from coloured LEDs particularly blue ones is because of the way luminious flux is defined, based on the perception of the human eye.
In fact if you take a look at a datasheet, say the Cree XP-E
http://www.cree.com/products/xlamp_xpe.asp , you can see that with Cool White you get 122 lumens at 350mA. With green you get 100 lumens at 350mA. The typical forward voltage is higher, 3.4 vs 3.2 so it's actually 1.19W vs 1.12W but even so if you're getting 122 lumens/1.12W white, do you really think you're going to beat 100 lumens/1.19W green with a filter which only outputs the same select frequencies?
Or take red where you get 56.8 lumens at 350mA. This may seem bad but remember these have a very low Vf, 2.1 typical at 350mA so we're only talking 0.735W. It seems you get about 140% at 500mA for red so you'll expect ~80 lumens. Considering Vf at 700 is 2.3V, 2.2 for 500mA must be roughly right so 80 lumens/1.1W. Again do you really think you'll achieve that with a white LED filtering the same frequencies?
Also if Cree or whoever can product greater efficiency by just using a filter on a white LED, don't you they might just do that? Okay it will increase cost but for those who really want the efficiency.
Note that your filter may allow additional frequencies and in fact this light could in some cases even look the same to the human eye. Or more importantly you may prefer or be happy with the different looking light. This complicates matters somewhat. But if efficiency is the aim, then generally speaking producing frequencies you don't want and filtering them out is unlikely to be efficient.
BTW AFAIK white LEDs aren't filtered much. They use phosphors but that's somewhat of a different concept. My understanding is we were talking about ordinary filters which simply cut off unwanted frequencies. I don't believe most filters are phosphor coated.
P.S. I suspect coloured LEDs are somewhat heldback by the smaller size of market meaning the money just isn't there. Particularly for green, red etc. Blue is perhaps not so bad so I presume some of the white LED research helps this.