Yes, they can! There are some PCP's that obviously can shoot much better (Daystate Redwolf, Thomas, Steyr LG110), but then you are also paying north of $2500 for that accuracy, and that price doesn't include the scope, so figure north of $3000 easily. That being said, PCP's are easier to shoot and will forgive a LOT of mistakes.
But if you want to really learn the gun, don't discount a good Piston gun. They force you to do everything right, all the way from hold, through the aim, and finishing up after the follow through. when you can learn to shoot a springer well, it will make you a much better overall shooter, regardless of powerplant.
I have two TX200's. Love 'em both. One has a 12 fpe venom kit in it. The other has a Tony Leach 22mm piston and is under 12 fpe. Both are smooth as silk to shoot and have excellent triggers. With the scope, you can put one together for right around $1000. Of course, I have a custom stock on each in order to accomodate my length of pull and to get the comb up to position my eye directly behind the center of the scope, so that upped the price a bit. But I also don't need any other associated gear that is associated with the PCP. AND, I haven't run out of air during a match yet with my springers!
I don't shoot off of sandbags or a rest. I shoot in AAFTA open piston class and when practicing, or setting up my guns/scopes, I use the sitting position with harness for all my shooting. My last practice outing, I shot a 10-shot, 25 yard group of 9/16". At 50 yards, that opened to exactly 1" for 10 shots. I had a little wind, but I was happy with those groups, which, in my opinion, is realistic.
What I like about them the most, is that they are so damn much fun to shoot! Each gun has its' own personality, and when shooting a match, and working the wind, it can be extremely satisfying when everything falls into place. That fun factor is something that you cannot put a price on. Conversely, shooting a PCP and getting near perfect scores all the time, can end up being boring as hell. Don't get me wrong, I have a number of PCP's, and shoot them well, but I really enjoy shooting my piston guns so much more.
I equate shooting a piston gun to driving a vehlcle with a stick shift. A PCP gun is like driving an automatic. Those who can drive stick don't lose anything to those who drive an automatic. It also makes you more aware of what you are doing.
There are a lot of guys and gals out there that shoot piston and know exactly what I am talking about. Those who discount a piston gun don't know what they are missing.