Can two transformers with different vector groups be connected in parallel?

Not unless you want to see some cool pyrotechnics!

Circulating current will be induced between the two Transformers if this is done. This current magnitude will be limited by the phase angle difference and the impedance of the two transformers. It is likely this current will be high enough to cause protective devices to operate regardless of loading on the secondary - fusing, overcurrent relays, sudden pressure relays, etc. If the impedance of the transformers is high enough, and the phase angle is fairly small (few degrees), LTC tapping may occur (some paralleling schemes use the circulating current between transformers to determine correct paralleled tap values). If they are "close enough" in phase angle, no serious problems will occur, other than (possibly) a small derate due to a small amount of circulating current.