Not at all.To them, it has to be false because if God existed then they would have gotten the life they want instead of the life they have. God and Jesus are supposed to be about "them".
For me, I think that the message is that no matter how bad things are now, we should be content knowing that God will make everything right. I think that this can kill empathy: after all, what reason could there possibly be to help somebody if the most capable entity in the universe has already said that he'd take care of it?
I think a good example of how harmful this can be is Mother Teresa: out of (austensibly) a desire to help the poor, she created a hospital where very few people actually got treated for their ailments - it was just a cleaner place to die. And it wasn't for lack of resources, either; she got massive donations, but she'd divert them to building her network of convents. And her patients wouldn't even receive normal painkillers, because of her misguided (but entirely Biblical) ideas that the suffering of the poor would gain them reward in Heaven.
In a very real sense, when the Gospel is put into action, people are harmed. If this was outweighed by some greater benefit, then I could understand, but any such benefit relies on the Gospels being based in truth... but I've never seen any reason to think they are.
Look at it this way: say you're at the scene of an emergency and someone shouts "don't worry! Help is on the way - an ambulance will be here soon!" If help is actually coming, great. But if it's not, and if the ambulance isn't coming but people will rely on the idea that it is, then the person who said it was coming has perpetrated a horrible, harmful act. If he knew that what he said was false - or even if he didn't know this but didn't have good reason to believe that what he said was true - then he's done something shameful and, IMO, evil.
And on a side note, I sometimes listen to the Christian radio station near here. They have a commercial that always leaves me scratching my head: it's for a "Christian financial planner" who says that he bases his approach on "Biblical principles." Whenever I hear his ad, my mind leaps to that passage quoted in the OP and I wonder how he could reconcile a profession where worrying about the future is the whole raison d'etre with a teaching that says, basically "don't worry about the future at all." Those two things seem fundamentally opposed to me.