air displaced from the point you teleport to is instantly moved to form a monolayer (1 molecule thick) on your surface.
The displacement of air is adiabatic (no heat is transferred, which will be true if the displacement is instantaneous)
Volume of displaced air: ≈ 100L = 0.1m^3 At atmospheric conditions: ≈ 4 mol
Surface area of cylindrical human: ≈ 1.58 m^2 Diameter of nitrogen molecule (which is roughly the same as for an oxygen molecule) : ≈ 3 Å Volume of monolayer: ≈ 4.7e-10 m^3
Treating the air as an ideal gas (terrible approximation for this process) gives us a post-compression pressure of ≈ 45 PPa (you read that right: Peta-pascal) or 450 Gbar, and a temperature of roughly 650 000 K.
These conditions are definitely in the range where fusion might be possible (see: solar conditions). So to the people saying you are only “trying to science”, I would say I agree with your initial assessment.
I’m on my phone now, but I can run the numbers using something more accurate than ideal gas when I get my computer. However, this is so extreme that I don’t really think it will change anything.
Edit: We’ll just look at how densely packed the monolayer is. Our cylindrical person has an area of 1.58 m^2, which, assuming an optimally packed monolayer gives us about 48 micro Å^2 per particle, or an average inter-particle distance of about 3.9 milli Å. For reference, that means the average distance between molecules is about 0.1 % of the diameter of the molecules (roughly 3 Å) I think we can safely say that fusion is a possible or even likely outcome of this procedure.