You can't draw 1A at 40V = 40VA from a secondary rated at 20VA.
What happens if you do? Is it physically impossible for the load to draw more or is something bad going to happen?
core material will saturate, output volts drops, power dissipation increases, too high and winding insulation could fail and shorting of windings causes larger further problems upstream.
Please don't spread misinformation:
In fact, core flux decreases, away from saturation, when loaded. Flux is a voltage thing, not a current thing.
The limitation is entirely thermal: the winding gets too hot and smokes.
Even that isn't a big deal, for some transformers, like the type pictured above. Small transformers, like these, are typically designed to operate into a short circuit for an extended period of time: they are "impedance protected". (And some contain a fuse too, which helps even more with safety.) The downside of this is, the output voltage varies widely with load current, and the efficiency is poor (perhaps 80% or less), so the transformer runs relatively hot, in spite its small size.
Roughly speaking, if you used only one winding, you could use about sqrt(2) more current through that one winding. The reasoning is as follows: the transformer is designed to dissipate P = I^2 * R watts in the secondary winding area. P is a design parameter, R is the DCR of the windings, and I is the rated current. (R and I are for both windings loaded, however you choose to connect them. If in series, then R is the total series resistance, and I is the current rating of a single winding. If in parallel, R is half the DCR, and I is twice the single-winding rating. The series and parallel ratings are usually stated explicitly in the datasheet, too.) If you use only one winding, then you can dissipate the same total power (which results in the same temperature rise), but instead of that power being split between two equal windings (dissipating P/2 watts), you can dissipate it in just one. This requires sqrt(2) times more current.
The actual figure will be less, because the windings aren't perfectly (thermally) conductive. In any case, you're throwing away 30% of your total transformer capacity -- you never have any reason not to use both windings.
Tim