15-dps (degrees per side) is fine for most folks on a EDC knife.
Without regard for should you do it ...,
1. take a look at where the stones in that sharpener make optimal contact with a blade in the sharpening position (somewhere forward of the outside edge most likely).
2. measure, or estimate how far from the front edge of the sharpener that location is.
3. measure, or estimate the distance from the sharpened edge on your knife to the front of the handle.
4. estimate how far from the handle the sharpener would effectively sharpen your prized pocket knife.
5. ask yourself "Would you think twice about running your edc through it for any particular reason other than a preference for manual sharpening?"
I believe you will see inside that powered sharpener that there are round wheels that apex (point of contact with blade) somewhere near the mid-point of the sharpener (or at least some distance from the front of the sharpener and the guide). With consideration for the ricasso and the handle on your mini Barrage, it would be my guess there would be a fair amount of unsharpened edge just forward of the handle. I suppose you could take the blade out of the handle to sharpen ..., but then there are just too many other simpler, better options that come to mind.
Kitchen knives typically do not have a ricasso and/or handle that interferes with a sharpener like this. Additionally, most cooks/chefs would not really have an issue if a small length of the blade just forward of the ricasso is not sharpened (unlike most of us ... with our smaller folders).
If you are still on board, with regard to thinking about doing so and/or using this sharpener for other knives ...,
Consider the primary grind angle and how that indexes in that Chef's Choice Sharpener. The side of the blade (the primary grind) indexes (lays against the guide) at an angle (unknown, presumably 15-degrees ???). Effectively, the primary angle (of the knife being sharpened) must be added to the angle of the guide (plus any additional angle the stone might be offset) to determine the actual sharpening angle of the stones or the effective secondary bevel. So the actual or effective secondary bevel is dependant on the primary bevel.
I just measured the primary grind on one of my wife's medium chef's blades at 2-degrees inclusive (1-dps). So that sharpener would effectively put a 15+1-dps or 16-dps secondary on this knife.
While I do not currently have a Benchmade mini barrage, I do have a Mel Pardue 5000 to use as illustrative. It measures 10-degrees inclusive (5-dps). So that sharpener would effectively put a 15+5-dps or 20-dps secondary on this knife.
I only bring this second point up, as I believe many folks potentially forget to factor in how a knife is indexed when sharpening, and assume this may play a part in your sharpening future.
I have a friend who sharpens his knives on a machine like this, and he I pleased with the results. Everybody has variable criteria for their own needs and uses.
The best way to learn, is through doing.
The best lessons cost time, money, or a combination of both.
If you "do" (sharpen your pocket knife on this machine) please post back the results for others to learn.