Are there any airliners capable of vertical climb with engine thrust only by pointing the nose up?
No, there are few planes that can do this at all. In order to be able to climb out straight up you need a thrust-to-weight ratio greater than 1. In other words you need enough thrust to propel the full weight of the aircraft up without the wings generating lift. 

Wiki provides a brief list of aircraft and associated thrust to weight ratios, the Concorde comes in on top at 0.372 with full afterburner but this is at max weight. Although at its empty weight it was pushing a 0.877 ratio. Even running on fumes would not have done it at full afterburner in the Concorde. For comparison the 757-33 has a ratio of 0.6 at Operational Empty Weight assuming a maximum thrust of 42,600 lbf per engine.