If you are in high altitude cruise, approaching a tropical storm cell with possible turbulences (but not using the "severe turbulences" procedure putting the A/THR off and fixing N1), what would be the selected mode ? Speed mode ?
Probably "Mach." Assuming the "High Altitude Cruise" part of your question and that speed is Managed, per the Airbus SOP (However unlikely that the company SOP may be different in this regard).
In speed mode, with airspeeds fluctuating down to a largely underestimated value (caused by a ram air port freezing of the Pitots for instance), would it be possible that the A/THR augment the thrust just before disengagement ?
I'm not entirely clear about what you're asking. But, with a downward speed trend, the A/Thr will react promptly (Somewhat) in "SPEED MODE" (Mach Mode with Soft Altitude engaged will be a slightly slower reaction), to the point of A/prot protection engagement (Airbus). Next, would be a pitch down command and TOGA commanded.
If yes, is it possible for the crew not to notice this level increase ? even in max thrust ?
Possible, yes. Likely, no.
Are there known examples of unusual behaviors of the auto-thrust systems both on Airbuses or Boeing's ?
I think a BA 777 crew could answer that question!
you might elect to decelerate toward your best penetration speed due to mod/sev turb expectations..
Just an FYI.....
Airbus FCTM 4.010
"...If moderate turbulence is encountered, the flight crew should set the AP and A/THR to ON with managed speed.
If severe turbulence is encountered, the flight crew should keep the AP engaged (Note: Good luck with that as the "G" load would probably keep knocking it out). Thrust levers should be set to turbulence N1 (Refer to QRH), and the A/THR should then be disconnected. (Interesting note: No reference to selected speed [obvious reason] in either FCTM or QRH)..."
Apparently, Airbus trains for two turbulence scenarios - Up to Severe turb (Everything Managed), and Severe or greater (Manage everything, but manual thrust).
Cheers