Help with circuit design.

[BigBoss]

No.
The outputs of a 741 opamp are very lossy emitter-followers. The datasheet shows a maximum 5V output voltage loss.
There is no -4.5V, it is a 9V battery. All the inputs are the 9V battery divided to produce +4.5V. Then the 741 opamps have a supply that is 0V and +9V.

With a 5V output voltage loss the output will be stuck at +4.5V and will not move. If the output of the opamp can swing with a 3V loss then it can go high to +6V and low to +3V. But then the output of the transistor emitter-followers will only barely swing high to +5.3V and low to +3.7V. The motor will get only 1.6V.

Output of LM741 has AB-Class Output stage, not a emitter follower.If you check the data sheet carefully, you will see that the OPAMP can work dual symmetric power supply.
https://www.ti.com/lit/ds/symlink/lm741.pdf
Otherwise principally it does not make sense to use this OPAMP.If the output stage was a simple emitter follower, you could not obtain a proper voltage headroom but it is not.
Output must be zero volt when any signal is not applied otherwise iif the output stage was a emitter follower there should have been a off-set voltage.

 

[Audioguru]

Output of LM741 has AB-Class Output stage, not a emitter follower.

The output stage operates with a small bias current to eliminate crossover distortion. Then it operates in class-AB.
It consists of an NPN emitter follower to produce positive going signals and a PNP emitter-follower to produce negative going signals. The emitter-followers produce a voltage loss of up to 5V. Almost all audio amplifiers have this complementary emitter-followers output.

If you check the data sheet carefully, you will see that the OPAMP can work dual symmetric power supply.
https://www.ti.com/lit/ds/symlink/lm741.pdf

ANY opamp can use a single polarity or a dual polarity supply if it is biased at half the supply voltage.

Otherwise principally it does not make sense to use this OPAMP. If the output stage was a simple emitter follower, you could not obtain a proper voltage headroom but it is not.

Correct. It is a stupid cheap circuit that might not work because it has no headroom.

Output must be zero volt when any signal is not applied otherwise iif the output stage was a emitter follower there should have been a off-set voltage.

The inputs are biased at +4.5V then the output will not be 0V. The schematic wrongly shows the opamps powered from +4.5V and -4.5V.
If the opamp is correctly powered by +9V and 0V then the output still will probably not be 0V without an input signal because there is no negative feedback and the opamp has an input offset voltage. The NPN and PNP emitter-follower outputs balance each other.