This group can cause a lot of trouble by doing what they have threatened.
They also get a lot of attention by simply threatening to do it.
They're already getting a lot of attention. They're basically executing the "Civil Disobedience 101" playbook, in particular by blockading streets, bridges, offices of those seen as wrecking the environment, etc. in strategically chosen locations. With a few exceptions the general public can just go around the scene via a different route with minimal disruption, but it requires a suitable response from the police, etc. to move them on so the authorities have to take note, which is the entire point.
A few of them might get a slap on the wrist type fine, but the media coverage (and there's been lots of it) has generally been neutral to slightly positive since they are almost entirely passive, with (so far at least) no serious violence from either side. For gnirtS's benefit, from the coverage and one of the protests I've seen it's also definitely not the "unwashed hippy" set making up the bulk, although they are present. There are a lot of quite prominent politicians, celebrities, parents with young kids, and older school kids taking part as well; it's a complete cross-section of the public that think more needs to be done for the environment, and fast. It seems to be working too; I've been noticing their logo not just grafitti'd onto the usual walls/bridges, but also on placards in house windows, farm gates, etc. quite a bit lately. Not too many, but definitely starting to spread.
Basically, I don't think they need to falsely claim to be about to do a stunt like this, and since they are pretty big on gaining more public support, I don't think the majority of them *would* do it. The public backlash against Gatwick was significant, and that's definitely not what they seem to be after. Maybe a hardcore set that is more militant and sees air travel as a major pollutant might (they should look at maritime shipping or some forms of construction some time!), or someone looking to use them to further some other agenda as a black flag operation, but the core of the movement? I just don't see it.