It depends. A variety of factors go into determining whether or not students are allowed to use calculators on tests. The content of the test, the math level of the students, and the duration of the test are just a few of the factors.
Every student, regardless of whether or not they are 'gifted and talented' should learn how to solve equations without the aid of a calculator. They should also learn how to use calculators as a powerful tool once they understand the mathematical concepts.
The decision to allow the use of calculators in a testing environment depends less on the students being tested and more on how the students have been taught and what the assessment is attempting to test. It is important to ensure consistency in the learning experience and testing environment, i.e. letting kids use calculators while learning and removing them for the test will distort the results. It will also distort the results if 'gifted and talented' students are not allowed to use calculators while the rest of the students are.
Calculators aren't inherently bad; if used correctly they can challenge students regardless of their math level.