Yes
If you measure the resistance of your motor you can calculate this current.
Example: let’s say the motor resistance is 12Ω and the motor power supply is 12v.
Your maximum current will be 12V ÷ 12Ω = 1A
If the BJT base current is 20 ma and the 2N2222 gain is 100 then in the simplest situation you can have 20 * 100 = 2A; our 1 amp is less than the 2 amp calculation.
Note: in cases like this we want the transistor to operated in saturation.
However, there is a maximum current that the BJT can safely operate at.
With our 2N2222 this is < 800mA (we must design for less than this).
So the 2N2222 will go up in smoke ? 
Well not necessarily.
When the transistor first turns ON the motor starts to move.
As the motor moves faster and faster, the current it draws can significantly reduce, perhaps down to 300mA or less; well with the operating parameters of the 2N2222.
Also, when the transistor first turns on, there will be NO current flow as the motor is an inductor.
As time goes by the motor current will increase from zero to a maximum level, it then reduces to a minimum running level.
During this power up interval, the transistor can enter a linear area where there can be significant voltage dropped across the collector to emitter of the transistor . This results in power loss and the transistor can get hot/be damaged.
The 2N2222 has a maximum power it can dissipate, < 0.5 watts with infinite heat-sinking, we must design our circuit to keep below this value.
With all this being said the OP should not be scared off experimenting, they should note there are limitations to what components can operate at.
The OP should be aware the transistor can get hot, many touch the case to see if it is hot but be careful 
If the OP intends to proceed with this as a hobby, a DMM is a tool they should invest in.