TW page 88: "A unit cannot lift off if it has a Safe Thrust of 2 or less." No exceptions are made. The section doesn't specifically mention support vehicles, however.
One of the real aero wonks may be able to provide a more complete answer.
That sentence refers to vertical liftoffs; thepreceding and following sentences in thesame parragraph make the context (vertical liftoffs) clear.
There is no minimum for an aerodyne (i.e. aerodyne small craft, ASF, conventional fighter or fixed wing support craft), though the craft in question would be theoretically unable to gain altitude; in effect, it would be a powered glider.
To wit, TW pp. 84 states that in order to gain altitude, an aerodyne must spend 2 thrust points. Not a problem for a 1/2 thrust aerodyne; after the necessary acceleration on the ground, the aerodyne is at altitude 1 on the low altitude map... no problem, that is, until you take into account velocity loss:
Turn 1: accelerating along the runway; turn ends at altitude 1, velocity 2
Turn 2: loses one velocity point, thrusts 2 forward; turn ends at altitude 1, velocity 3
Turn 3: loses half velocity, rounded down (2 points) - three choices: A) land, B) 2 thrust forward, remain at altitude 1 for remainder of the flight, C) attempt to gain altitude (choose C): spend two thrust to gain one altitude; turn ends at altitude 2 velocity 1
Turn 4: loses half velocity (one whole point); starts the turn with velocity 0; if the aerodyne has VSTOL capability, no problem (aerodyne can continue spending thrust to either gain velocity [max 4] or altitude, if not, the aerodyne stalls, dropping one altitude level (to altitude 1) and forcing a control roll (failing this roll would be
Badtm); even if it makes it, the aerodyne would be stuck in the cycle of trying to gain altitude.
Of course, if the runway was at the edge of a cliff (of low altitude proportions), the non-VSTOL aerodyne could choose to drop 2 altitude levels in order to gain a velocity point, so that in a subsequent turn the aerodyne could end a turn with a velocity of 4, thus it would start the next turn with a velocity of 2, which would allow it to spend its entire thrust (all two points of it) into gaining altitude; thus it would operate as follows:
Turn 1: end of runway: altitude 1*, velocity 2
Turn 2: velocity 1 / 2 thrust forward (over the edge of the cliff); altitude 1, velocity 3
Turn 3: velocity 1 / 2 thrust forward, descend 2 altitude levels (free); altitude -1, velocity 4
Turn 4: velocity 2/ 2 thrust to climb 1 altitude level; altitude 0, velocity 2
Turn 5: velocity 1/ 2 thrust forward; altitude 2, velocity 3
Lather, rinse, repeat.
*for reference; the runway could be at a higher altitude OR the cliff could be over a DEEP precipice
Note that it can either maintain altitude or drop altitude; a non VSTOL 1/2 thrust aerodyne is a powered glider.
OTOH, a VSTOL-capable 1/2 thrust aerodyne could actually gain altitude up to and including the atmospheric boundary on the high altitude map (they can't climb higher since they can't spend 4 thrust in a single turn).