<p>I'm currently attempting to  make a repstrap using paper printed parts, like this guy : <a href="http://www.mariolukas.de/2012/05/repstrap-3d-drucker-aus-computerschrott-teil-1/" rel="nofollow noreferrer">http://www.mariolukas.de/2012/05/repstrap-3d-drucker-aus-computerschrott-teil-1/</a>
I replaced the DC motor in a paper printer carriage assembly</p>

<p>with a stepper motor (NEMA17). But there was not enough space to fit the axis of the nema 17 at the exact spot of the older DC motor axis, in short, the axis are not in the same place. The question is : if the axis is not in the exact same spot, will it affect the movement of the carriage or not at all ?<a href="https://i.stack.imgur.com/8A21q.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/8A21q.png" alt="new and old belt driven axis"></a></p>

<p>I supposed it would but i'm not sure since the carriage is limited in movement by the rails and that we still move the belt around.</p>

Axis should definitely be at proper position. Otherwise you will get at least 2 issues.
Carriage will be pulled up which will cause stresses on rollers or slides and it will stress your belt
The way the carriage will go will change but because carriage itself is fixed then it will change the speed
3D printing is a precise process. Both issues will have impact on printouts and all your printouts will have broken dimension in the axis in which carriage moves.
Have a look on the picture (it is big to show details)
fig A
shows a situation where carriage is far from the axis
In such situation the distance between vertical line of black cross and pink circle is almost unnoticable so both - the force and the distance (so speed) change are very small.
fig B
shows a situation where carriage is relatively close to the axis
Then both - the force and the distance change is noticable