Precision when changing ring dimension

Is my understanding that the ring dimension affects the security level of the encryption, but not the precision, correct?

That is, can I test a code using a low ring dimension, and then move to production only changing the ring dimension and expect the behavior to be the same, except slower?

If it’s relevant, I’m using the CKKS scheme.

Thank you.

Please refer to the second part of this answer For the SingleKey Architecture, I only achieve a 128 security level with a ring dimension of 31k - #2 by Caesar