It will work yes, but after you've done that you really want to beeline towards Guilds. Also ensure you grab your luxury techs. The beauty behind the Netherlands is that you can sell off luxuries even faster then other civs can without dipping into (too much) unhappiness. So delaying the NC beeline just a wee bit in order to snag up that Marble or such may not be a bad idea, as it allows more rush buys.
Once Guilds (and by extension Polders) get online, your cities will be enjoying a massive boost - even just 2 or 3 polders will do great things for you.
Marshes aren't detrimental to your start - well, early game they'll be somewhat annoying, but don't remove them and work other tiles until you can make them into Polders.
That said, the Netherlands are at their best when you manage to secure a few great Desert spots - not the ones you'd normally go for with Petra, but those with at least 6 Flood Plain tiles you can turn into Polders. Those become some of the best tiles you've ever seen (Rivalled only by Incan Terrace Farms IMO). A Desert start with the Netherlands basically means you're going to get a huge Amsterdam, no matter what.
Also, ensure you have at least one coastal city. The Sea Beggar is too good to ignore.
Puppets are amazing for Netherlands due to access to even more money and luxuries for sale. You'll want to be careful in your aggressions though as good diplomatic relationships are important in your selling luxes game. Fortunately, the huge cities you can get with Polders offset the lower amount of puppets one tends to have as the Dutch. Militaristically, the Dutch are also the ONLY civ without any bonuses on land military, so do keep that in mind.
...yeah, I play as the Dutch very often

Have fun with them.