Off the shelf Manganin would very likely not have the similar TCR as the resistors in your instrument, stock Manganin has a TCR of ±10ppm/°C to ±20ppm/°C and the curve is hyperbolic around the 25°C reference point. Those Manganin resistors went through a set of specific bakes and stress relief procedures to produce very low TCR....and note, to some degree it was hit or miss, in other words the resistors after processing were measured, their individual TCRs noted and then matched together for TCR that met the required specifications.
At one time winding by wire length was generally used to wind resistors, the ohms/foot was noted, the required resistance was divided by the ohms/foot number resulting in the approximate length of wire required for a given resistor value. The resulting resistor still had to be 'calibrated' to the correct value/tolerance by removing wire from the bobbin until the value was satisfactory and then could be terminated. Unfortunately it was found that winding by length measurement was difficult and in the case of the very fine gauges virtually impossible due to wire breakage during winding. The practice is not that common anymore.
If I understand your question correctly, the general answer would be no unless the tolerance was rather sloppy, if you were referring to essentially what is called wind and terminate.
One other factor that needs to be considered in divider strings is the variance in power dissipation among the resistors (if they are of differing values), the easiest condition is where the divider resistors are all the same value then dissipation becomes somewhat less of a thorn. If they are of different values then the power dissipation of each resistor must be considered to determine the effect of self heating on the resistors, this will cause an apparent difference in TCR even if the resistors have the same identical resistance and TCR.
Integrated resistor networks do reduce the dissipation difference to some degree but is rarely, if ever absolute among the resistors. Probably the more important condition is that the temperature around the resistors remains as stable as possible thereby keeping the resistors at a stable operating point minimizing drift.
Manganin is one of the few resistor alloys that can be soldered, the prevalent Evanohm alloy requires welding to terminate.