Since the thrust increase in this case is proportional to the mass increase you should end up in the same spot excepting a minor difference in induced drag.
True, as long as the AOA one needs to maintain does not change the "efficiency" (i.e. lift/drag ratio) by much, you will end up in the same place, only faster.
The physics of gliders is quite interesting, especially from the energetic point of view. Consider this: if you hover in one spot, you potential energy is constant and your kinetic is constant (0) - there should be no energy input required in order to hover... The requirement for an energy source is introduced in the fine details of the force balance. In order to resist gravity, one has to "push", or in the glider case more like "lean" against something - air. This requires one to move air about which immediately introduce viscosity and turbulence into the picture - an energy that the plane will deposit into the air and never get it back.
Without thermal winds, the glider has no energy source. It can only cash its banked potential energy into kinetic energy (from the gilder's point of view, making the air move so it can lean against it). And here is the interesting part - the gilder does not spend energy in order to stay up, it spends the energy in order not to slow down. Sounds the same but it is conceptually different: the energy that is required in order to keep a craft hovering using a rocket or Harrier style jets is HUGE compared with the energy required to keep a plane flying level by moving the air over the wings and paying for the drag. The wonderful "magic" of aerodynamics versus brute kinematics. This is why I say that gliders and planes "lean" against the air rather than "push" it.
The description of the ability to lean on the air versus the price tag of the drag is folded into the lift to drag ratio (L/D) which is the aerodynamic efficiency. Without going into details, this is nearly constant for much of the range of AoA and velocity (increase of lift increases drag nearly proportionally) and this is what controls the glide angle. The mass does not appear there explicitly. It has an implicit effect of requiring larger and larger AoA and higher velocities that eventually moves the plane out of its optimal L/D and the angle steepens. Fighters can glide at a surprisingly shallow angle, but they do it at very high speed which leads to rapid loss of altitude simply due to the speed, not because they truly fall like a brick.
