Does the amount of energy released from burning of fossil fuels have a measurable impact on global warming?
Yes, it does add to global warming.

No, it's not currently measurable.

Human primary non-renewable energy consumption is about 15TW - and pretty much all of that goes into low-grade heat in the ocean surface and the atmosphere.

Expressed in the same terms as the forcing units of global warming, the forcing effect of that heat is about 1.7% of the effect of the anthropogenic release of $\ce{CO2}$ to date.

So we can calculate it, but it's not directly measurable as a change to global energy content: it matters, but it's not quantifiable from temperature observations, given current data and techniques.

(Kudos to Pont for the link to the paper)