convolution of a real and complex signal
You are confusing several different notions. First of all, two signals $x(t)$ and $y(t)$ are orthogonal if

$$\int_{-\infty}^{\infty}x(t)y^*(t)dt=0\tag{1}$$

From (1) it is clear that if two real-valued functions $x(t)$ and $y(t)$ are not orthogonal, i.e. the integral in (1) is not equal to zero, then also $x(t)$ and $jy(t)$ are not orthogonal. So your argument that the two given signals must be orthogonal because one of them is real-valued and the other one is imaginary is wrong.

Furthermore, even if two signals are orthogonal to each other, their convolution is usually non-zero. Just take two rectangular functions that do not overlap. Obviously, they are orthogonal, but their convolution is a triangular function.

Consequently, one way to interpret the convolution of the two sinc functions is that a low pass signal with cut-off frequency $W$ is filtered by a low pass filter with cut-off frequency $2W$, and multiplied by the (irrelevant) factor $-j$. Since the low pass filter has no effect on the low pass signal, the only change to the signal is the constant factor $-j$.