There is no direct method, but there are two ways of achieving this.
First, it can be done using the image analysis window (Windows > Image analysis). Select your image, then apply your function (fct button in "Processing") on it. To select a function (in your case, "composite band" and/or " grayscale"), right-click on the identity function and select "insert"). Mainly interesting if you have many functions to apply.
On the image, you see my "on the fly" grayscale image from a multispectral image.
The other method consists in computing your grayscale image (band1 + band 2+ band3)/3 in raster calculator with an in memory output. No need to create a composite raster before.
As a remark, slightly out of ArcGIS, ArcGIS supports the vrt format. So you could also create a vrt and open it in ArcGIS.