No
Most content owners do not file criminal charges any more these days, since extorting people for cash is far more profitable (and less likely to generate bad PR) than filing criminal charges.
Also, the German system works in the way that e.g. in a bar brawl first you file criminal charges (here: assault), then the aggressor gets sentenced to jail or fine (to be paid to the state), and then with the verdict you go to a civil court and sue the aggressor for damages.
If I understand US courts correct, they summarize both into one court.
Downloading illegally-distributed files is illegal in some jurisdictions (but not too many, mostly only uploading - i.e. distribution - is illegal). That's true. So, use of Popcorn Time (or clones) for illegal things could be, indeed, illegal.
Also, in some jurisdictions linking to illegally-distributed content is illegal. Now, that's exactly what Popcorn Time does. So the point is valid - the very software (and its distribution) could be ruled to be illegal as well. Just as, say, Napster. It's just that Napster could be shut down for good and Popcorn Time couldn't - due to decentralized nature - but that's not a legality issue anymore.
However, what's very likely to be not illegal here is a development of the said software. There's very unlikely to be such a meta-law that forbids the very development of software that may result in linking to illegally-distributed materials. Sometimes there are attempts to apply a anti-malware laws, but that's quite a big stretch that works only in corrupt and/or ignorant courts (like some in Russia).