None of the areas in the East Indies spoke Dutch. However, the Dutch were not above learning the local lingua franca, Malay, which helped them a lot when it comes to competing with other colonial powers.
Again, the Dutch never went into a state of total war in the Indies until the Java War in the 1820s. Before that they've used their war-chest for divide et impera. Even the greatest landgrab in the 1740s was achieved by allying themselves with the vassals of the Mataram sultanate who were less dependent on trade, and thus shared a strong anti-Chinese sentiment with the Dutch. Simply the idea that the Sultan was going to side with the Chinese rebels against the VOC was enough to mobilize the Duke of Madura's large retinue to invade and cause havoc in the pro-Chinese coastal duchies where most of the Sultan's manpower and income were concentrated. To be clear, the VOC was losing before they made an alliance with the Madurese, partially because the Governor General was going insane. When the dust cleared though, Java wasn't ready for a second round. Then they tricked the Madurese (who were descending to a state of infighting as well) into signing a treaty very favorable to the Dutch.
This was the MO of the Dutch all over the Indies. Supporting pretenders and rebels, tipping the balance between rivalling factions, using the lust for power of inexperienced native leaders, etc. European troops was also never even half of the soldiers the Dutch commanded, they had slave warriors, mercenaries, native allies and later local conscripts to do their dirty work for them. When it's an even playing field, the Dutch indeed struggled, such as in South Borneo, Jambi, and of course Aceh. I would argue that the political landscape in Mexico would allow the Dutch to use a similar strategy. Integration would be gradual, just like in the East Indies, and they would never in a million years achieve a settler colony there, but why bother? Dutch dominance in trade would be achieved anyway and that was their only goal.
As for the navy, well they sure could use some jumping off points. However, the Dutch navy in its prime could take on the English any day of the week, no sweat. They won the third Anglo-Dutch wars even when they were gangbanged from all sides.
I could have missed a few factors, though. So this is all hypothetical. In any case, the Dutch in their golden age didn't need a lot of manpower, they were rich and devious enough to make up for that.
Edit: also, the PoD would need to be quite early, if other powers had cemented an effective rule, I don't think the Dutch could dislodge them. It was easy for them to kick the Portuguese out of Malacca and the Iberians out of the Moluccas, the same can't be said for the Philippines.