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No. In general case Mat's type is unknown in compilation time.

You can use template class Mat_:

template <typename T> void func(Mat_<T> img);

cv::Mat_<float> mat;
mat.create(rows, cols);
func(mat);

or use switch/if construction:

switch (mat.type())
{
case CV_8UC1:
    {
        uchar* ptr = mat.ptr<uchar>();
    }

case CV_8UC3:
    {
        Vec3b* ptr = mat.ptr<Vec3b>();
    }
}

or use table of pointer to functions

typedef void (*func_ptr_t)(Mat img);
func_ptr_t funcs[7][4] = 
{
    {&func_8u_c1, &func_8u_c2, ...},
    ...
    {&func_32f_c1, &func_32f_c2, ...}
}
funcs[img.depth()][img.channels() - 1](img);