The hose provides manifold pressure to open the wastegate and prevent excessive boost from the turbo. The spec is about 12 psi as a limit.

Without the hose, the turbo can probably get over 20 psi. There is a safety "overboost protection valve" on the firewall that should dump fuel enrichment at a manifold pressure of 15 psi and effectively drop the boost.

A cracked hose will usually function in similar manner to a integral hose, provided the hose is relatively intact. The SD had a similar situation recently and it never reached unsafe boost levels AFAIK.