Noise from test pins on signal lines?
The only answer is "it depends". If you use 20bit 100Hz ADC, proper filtering would mitigate any test points.

Other than that more details is required. With 20bit i guess you are mostly afraid of the mains 50Hz coupling. But other sources of interference may be there as well. 

Best advice- do everything best you can. Use good cables, ballanced differential lines, and keep budget for the second layout.