A similar thought experiment would suggest that angle of climb, relative to the ground could be increased when flying into a headwind by climbing at an airspeed below Vx.
DISCLAIMER: I am not in any way suggesting that a pilot should actually do this in flight. It would be a very bad idea, would wouldn't likely produce any real gains. I'm just saying that technically, some small increase exists.
Take a hypothetical airplane with a Vx of 60 knots. Now consider departing into a constant 50 knot headwind. If you climb at Vx of 60 knots, you will have a forward airspeed of 10 knots, so your effective angle of climb, relative to the ground will be something less than 90 degrees. If you were to pitch up and slow to 50 knots (assuming that you didn't stall and drop out of the sky) Your forward groundspeed would now be zero, so (again, assuming that you have a positive rate of climb) your climb angle, relative to the ground, will be 90 degrees, Obviously, a 90 degree angle of climb is steeper than an angle of climb less than 90 degrees.
Now, I'll reiterate, I am not suggesting that operationally, this effect can be used. At wind-speeds which are not close to Vx, the gain in angle would be negligible, or even negative and more importantly, climbing at an airspeed less than Vx is a really bad idea. A true Vx, if Vx is actually published, results in a pretty nose high attitude. and in a lot of GA airplanes its is getting fairly close to stall speed. A sudden loss of power would require an immediate, aggressive pitch over maneuver to keep the airspeed from decreasing rapidly. If you're climbing at a speed les than Vx, you're that much close to stalling, you have less kinetic energy, and your pitchover is going to have to be even faster to avert disaster.
I have been told, that Cessna no longer publishes the actual Vx for their single engine aircraft, instead they have a "recommended obstacle clearance climb airspeed" or some such, which is actually a little faster than true Vx. Their reasons for that change were because of the steep pitch attitude at Vx and the hazards that creates in the event of an engine failure.
I don't know for certain this is true, but when I first heard this some years ago, I looked at a number of Cessna 172 pilots manuals from different years, and there was indeed an increase in the climb speed and a change in the phrasing thereof across model years where it wasn't apparent to me that there was a real change to the aircraft which would result in a real change to actual Vx. That seems to support the claim.
So, in case I haven't been clear: really bad idea to be mucking around climbing out at airspeeds less than Vx. DON"T DO IT.