Could battlecruisers protect convoys as distant reaction forces?

Could a battlecruiser remain clear of a convoy, then rush in after a raider revealed its position?

Only unreliably. A raider could jam the convoy's transmissions, leaving the distant battlecruiser without a timely location to intercept.

The proposal preserves the battlecruiser's speed but creates a command-and-control problem. A convoy under attack has to send an accurate position through communications the raider may disrupt. Without that report, a fast reaction force does not know where to concentrate. Paper speed cannot substitute for local protection when detection and radio links are uncertain. Convoy defense is therefore a system of escort position, communications, and response time rather than a race between isolated ships.