Why old battleships remained useful in the First World War

Would a large reserve of pre-dreadnought battleships have been useful when the First World War began?

Yes. Their secondary missions made them force enablers, and reserve status kept usable ships available without wearing out the active fleet in peacetime.

Pre-dreadnoughts could support the army in Flanders, bombard Gallipoli, transport troops, guard ports, and reinforce local defenses. The Royal Navy therefore moved useful ships into ordinary reserve rather than scrapping them merely because newer battleships existed, returning some to front-line work in 1914 and preserving the modern battle fleet for tasks only it could perform.