It is. And it is not.
Electricity markets are generally not set up for the demand-side to do much active participation at all. So the short-run demand curve as seen in, for example, Nordpool Spot, is almost perfectly inelastic. Not quite, because there are some large industrial demands that exhibit some elasticity, and are exposed to the spot market. But a very large chunk of demand isn't exposed to the spot market at all; and a lot of the demand that is exposed, is highly inelastic - particularly to half-hour-by-half-hour changes.
That tells us a lot about the structure of the markets, and only a little about the actual underlying demand curve.
Until there's a lot of demand-side response (DSR), we've only got stated-preference studies and DSR pilots to go on, to estimate what the demand curve would look like in a well-functioning market: the evidence we have (e.g. from the Olympic Peninsula study), suggests there's quite a lot of potential demand elasticity out there, just waiting to be harnessed. Note that when short-run demand elasticity has been observed, it manifests in two ways: some demand will move between half-hours that aren't too far apart, when the price differentials incentivise it. Some other demand will just vanish altogether when prices rise.
If you want to try to distinguish the elasticity signal from all the noise in the existing market, then you need to take demand and prices for a particular half-hour slot on Tuesdays-Thursdays in one particular season across several years; and look at how weather-adjusted demand varies with price, while adjusting for any long-term trends.