Not likely. HDMI is a DIGITAL signal. VGA is an ANALOG signal. You can shove as many adapters as you want in that chain, but at the end of the day you're still pushing digital data. The converter box is what CONVERTS (with adapters built in) the signal from digital to analog.
For reference, DVI to VGA adapters exist because some DVI cables (not all) can carry analog signals. This is because the original source is pushing analog, so there's nothing to convert. (look up DVI-D vs DVI-I vs DVI-D).
tldr: while you may be able to physically connect your two devices together (source and destination), you will need to convert the digital signal into an analog one
Having said all that, I just looked at the link in your comments (HDMI to VGA convert) and apparently a cable does exist for that (the extra red/white connectors are for audio). I haven't researched this cable at all, but I am currently skeptical of it.
FOLLOWUP: That cable specifically states it does not work with a laptop/computer. It also conforms to what I stated above: it does not convert signals.