Yes, although the 3dcalc expression is a little clumsy. The method is to (1) convert the z-statistic to its CDF value and then (2) convert that CDF value to a t-statistic with the desired number of degrees of freedom (DOF) -- you need to supply the DOF parameter.

The expression is like this

"cdf2stat(stat2cdf(x,5,0,0,0),3,DOF,0,0)"

where DOF is the degrees of freedom parameter. Generally, this would be one of the following:
1-sample t-test: number of input datasets - 1 - number of covariates
2-sample t-test: number of inputs in setA plus number of inputs in set B - 2 - 2*number of covariates
However, special cases are the 2-sample paired test (which is really the same as a 1-sample test) and the 2-sample unpooled variance estimate (where the DOF varies among voxels, and you might as well use the standard 2-sample formula above).

A sample command to see the effect of this mapping function is:

1deval -xzero -4 -del 0.01 -num 801 -expr 'cdf2stat(stat2cdf(x,5,0,0,0),3,10,0,0)' | 1dplot -xzero -4 -del 0.01 -stdin -xlabel z -ylabel 't(10)'

I set the DOF parameter to 10 here so you can see the effect. For larger DOF parameters, the effect gets smaller -- that is, the graph of t vs z gets closer to being a straight line.