Yes. When I say fakes are equal weight in this answer I mean they have the same weight as a normal coin.
Put 24 coins on one side of the scale, and 24 on the other
I will address this in two cases, first, if the scale doesn't tip:
You know you have fake coins in each pile, or the fake coins are equal weight
Divide one side of 24 into two piles of 12 and weigh these. One of these piles must contain one and only one fake (or two but they would have to weigh the same as normal coins, so we can easily check this)
If the scale tips one way:
The fake is lighter, or heavier but not the same
If the scale doesn't tip:
The fakes are equal weight
So now you know if they're the same weight, and have used at most 2 weighs. If they're not the same weight,
Weigh your two piles of 12 (record which way the scale tilts).
Select just two coins at random from the pile and place them on one end of the scale. Then put two other coins at the other end. Record which way the scale tilts.
If the scale tips one way
Then take off the coins you just put on one side of the scale and put two different coins on the scale. If in this weigh the scale stays the same then the previous coins were fake, and the direction the scale tilted indicates their weight.
If the scale doesn't tip, repeat this previous step 3 times at most (5 weighs in total at most), and:
You will either have had a trial containing the fake coin and will know which coin is fake by the way the scale tilted after adding (as per above). Or, if you haven't, then you chose the pile of 12 that didn't have a fake, and that means in the first test (with the two piles of 12), if the scale tilted down towards the pile you were just testing, the coins are lighter, otherwise heavier.
Now for the case when weighing the 24 piles if the scale does tip:
Split into four piles of 12, and place one pile of 12 on one side
Place each of the three remaining piles of 12 on the scales. If it tips for one but not the others, then the direction the scale tilted for that one trial indicates if the coins are heavier or lighter.
To divide into two groups. After performing your trials:
If in the first weigh of 24 they are equal great, you have your groups
You have groups of 12 after the second process, and you know by weighing which ones contain fakes. In this case, you combine the two fake groups with the two non fake groups and voilla, you have two sorted groups.
Sorry if this is hard to understand, I write in code, not in English, so it was hard not calling functions to express this :P