For a particular LED? No.
A quick web search for "broad spectrum IR LED" threw up the following interesting news release, Osram presents the world’s first broadband infrared LED from 2016.
Osram Opto Semiconductors is using converter technology for infrared emitters for the first time. The result is an LED that emits broadband infrared light in a wavelength range from 650 to 1,050 nanometers (nm). The main application is near-infrared spectroscopy, for example for analyzing food.
Further down the technology is explained thus:
The basis of the SFH 4735 is a blue 1 mm2 chip in UX:3 technology. Its light is converted into infrared radiation with the aid of a phosphor converter developed specifically for this application. A residual blue component in the light helps users target the area they want to investigate. The emission spectrum of the SFH 4735 has a homogeneous spectral distribution in the infrared range. The chip is mounted in the proven and compact Oslon Black Flat package which is characterized in particular by good thermal resistance.
Checking the SFH4735 datasheet, the Vf is 2.95 V at 350 mA which ties in with the blue LED as IR would typically be 1.4 V for the low power devices at least.
They're quoting 60 μW/nm @ 750 nm and 30 μW/nm @ 980 nm. (The article is missing the '/nm' in the units.)
€6 each on Digi-Key.
Prompted by @asdfex's comment I had a look further down the datasheet and the relative spectral emission is quite horrendous.
Figure 1. The relative spectral emission graph shows a blue peak at >> 100 times that of the IR.