Can a Dy11 vector group transformer be connected to a Yd1 vector group transformer source?

In series, yes. In parallel, nope!

Putting a Yd1 transformer in series with a Dy11 transformer would result in the output of the Dy11 transformer being identical to the input of the Yd1 transformer with the exception of the voltage magnitude - this will change depending on the winding ratio's on both Transformers.

But, in regards to other properties of the voltage, the phases will in be in phase, with the voltage in-between the two transformers lagging by 30 degrees.