I'm in the camp that thinks arena is worth it for everyone. Here is why.

To "break even" on value, you have to go 3 wins. At this point you average about 150 gold worth of value. This doesn't mean you get that much gold, but it means, on average, you get the 100g worth of a pack plus that much value in dust or gold. As a new player, dust lift seem less enticing, but technically you can count 1 dust = 2 gold. Doesn't perfectly work like that, but it works for rough values.

So. Now you know going 3 wins will break even. But what happens at less than that? Even at 0 wins 3 losses, you still average about 130-135 worth of gold. Rewards can certainly come out to less than that, but still, you average about that much of value.

So now the question becomes "even if I do the worst that I can, is the arena experience worth about 15 gold to me?" And if that answer is yes, it's worth it. Because you won't usually go 0-3. It will happen sometimes, but not usually. And when you do go 3+, you will end up getting your value back.

The other caveat I will add... If I could give you one bit of advice, it would be to use either a program like HearthArena, or one of the arena charts online that rank the value of each card. Especially for new players, but even for experienced ones, it is really difficult to accurately gauge each cards value. Some are better in arena that just don't seem like they would be. Using one of these drafting charts or programs to help show you the value of the three cards you will pick will be the single thing you can do to start quickly getting a 3+ win average. Just realize that the "average" arena player doesn't do this, so don't so will help give you an edge. It will also teach you a lot over the long run about what cards are good and why in arena. Just know that doesn't always translate to constructed.