How would the presence of Royal Netherlands Navy battleships have impacted on the course of WWII ? Any which were in the Atlantic would probably have joined the rest of the Dutch fleet in British ports (as occurred after Queen Wilhelmina and her govt were ferried to England just before the Netherlands capitulated), and would've been attached to the RN to participate in such ops as the hunt for the BISMARCK in 1941, convoy escort duties to Murmansk, and providing fire support for OVERLORD in June 1944- provided they weren't lost to the Luftwaffe early on. Given the Dutch govt-in-exile being quickly established in England and supported by a fair armed forces contingent, I doubt that there would've been much of an issue re the possibility of the fleet falling into enemy hands as occurred with the French Navy and Mers-el-Kebirs et al.
OTOH, if there were Dutch battleships in the Pacific, they could've been sent to the bottom with HMS PRINCE OF WALES and REPULSE in Dec 1941 had the NEI command decided to deploy their major naval forces- as they did OTL with their cruisers, subs and bombers- in forward defence to assist the British defence of Malaya. Or what about if these capital ships were held back to participate in the Java Sea ? What impact could Allied battleships (of which there were none available after Pearl Harbour and the loss of PRINCE OF WALES and REPULSE) have had on the impact of the war in SWPA at that early stage, provided of course they weren't sunk 1st ?