It definitely paid off, and rather quickly to boot. Oil has several major advantages over coal. It is a better store of energy, with one kilo of oil containing 44,000 KJ of energy, compared to 33,700 KJ for a kilo of the best coal available. It was easier to load, store, and feed into the boilers, leading to a reduction in the number of stokers required. It also allowed for easier control over smoke production. On coal's side, it was initially cheaper and easier to supply, and the coal bunkers provided useful extra protection. It was also possible to extemporise additional coal storage, by loading bagged coal, which couldn't really be done with oil. The last coal-burning class of destroyer used by the RN were the 1908 Beagle class. A comparison of these with the 1911 Defender, of comparable power and capability but using oil, is illustrative of the difference:

| Beagle (Coal) | Defender (oil) ---|---|---- Boiler surface (sq ft)| 26,000| 19,000 Boiler room weights (tons)| 187| 142 Boiler room length (ft)| 92 | 61 Total machinery weight | 345 | 300 Ship length (ft)| 270 | 240 Fuel weight (tons)| 225| 175 Endurance (nautical miles)| 2200 at 15 knots| 2600 at 13 knots Engine and boiler room complement| 58| 24 Speed (kts)| 27.2| 28.5 Cost (£)| 106,000| 83,000

As should be clear from the table, the oil-burning ship could be smaller, cheaper and have less crew operating it, while still remaining as capable as a coal-burning ship. It also allowed for easier expansion - an oil burning ship with the same weight and amount of machinery could reach speeds that were impossible with coal. As the expansion of oilfields continued, and civilian consumption of oil increased, oil became more available and much cheaper, meaning that coal lost all advantages it had over oil.

Source:

The Grand Fleet: Warship Design and Development 1906-1922, David K Brown, Seaforth, 2010