The sample size formula for a one-sample t-test is often given as:
$$ n = \frac{(z_{1-\alpha/2} + z_{1-\beta})^2 \sigma^2} {\Delta^2} $$
Meanwhile, G*Power appears to use the t-distribution, which gives larger $n$'s because of the heavier-tailed t-distribution. This strikes me as more accurate since we'll be using the t-distribution for testing. Is using the normal quantiles to calculate sample size then underestimating the necessary sample size for a given power and type-I error?
A typical way to use the sample size from the normal assumption would be to approximate the number of degrees of freedom in the t-distribution. Say your sample size calculation, using the normal distribution, gives a required sample size of 60. You would then use $n=60$ and $df=59$ in the sample size calculation with the $t_{df}$ distribution.
Yes, you underestimate the required sample size when you use the normal distribution, which underpowers the test. Whether or not this loss of power is worth going through the extra work of estimating the degrees of freedom and then redoing the calculation (a process you might iterate several times) will depend on the problem and the people working on the problem.
