At second level, I think they might have a shot -- if at least half the party had their dailies. It could go either way, but without some of those big powers, then it will be tough. What is the breath weapon of the other dragonborn?
My limited experience, they'lll lose, although (depending on terrain) they may be able to escape.
Also, a black hatchling is a pretty boring opponent. It has very high defense (eg AC, Defenses against special attacks) but does lame damage, so the fight just lasts a long time. When the PCs do a ridiculous amount of damage to it and realize it isn't even bloodied yet, they would probably flee.
I ran into the same issue with
Kalarel in Keep on the Shadowfell, made worse because the one PC he could keep hitting was resistant to some of his best attacks and he had no recharge powers.
dragonborn breath is a encounter, not a daily. This is really important.
My level 1 party, who arent really into powergaming mind you, defeated a level 4 solo at level 1 after going through 6 level 3 encounters without an extended rest. They rolled okay, but not poorly or exceptionally.
Either they are superhuman or this fight should be very doable.
The impact of the lack of daily powers depends upon whether they had great daily powers or not If they are missing out on Brute Strike, Acid Arrow and Bastion of defence, it isn't much of a loss. If they are missing out on villains menace, lead the attack and flaming sphere then it is a bit of a disaster for them!
It will take them ages to whittle down the dragons hit points, and if the dragon concentrates on taking them down one at a time (and has a bit of luck with its breath recharge) it should take them down without too much difficulty.
I ran the Scalegloom hall and the party was lucky to win, in fact all the party was down in the end with the dragon on 7 hp when the ranger rolled a 20 on his death save just as the wizard was dissolving due to the breath weapon.
Even so it was was Pain of Death that really finished off the dragon in combination with Divine challange. That and action points, where the strikers were able to do dailies and encounter power back to back.
That said I ran the dragon badly, first time running D&D 4. Now, I'd run the dragon better and with its hide and darkness it would be much tougher.
If the dragon has places to hide and attack from then the party is hosed otherwise they might shade it but it will be a knockdrag down fight.