No, Dutch deaf and hard of hearing people generally do not understand American Sign Language (ASL). ASL is a distinct language from Nederlandse Gebarentaal (NGT, Dutch Sign Language), and the two are not mutually intelligible. While some Dutch deaf individuals may know some ASL, it is not widely taught or used in the Netherlands.
NGT and ASL are completely separate sign languages, with different grammar, vocabulary, and cultural roots. NGT developed within the Dutch deaf community, while ASL originated from French Sign Language and evolved in North America. Even though many hearing Dutch people speak English fluently, that bilingualism does not automatically extend to sign languages. A Dutch deaf person who knows NGT would understand ASL about as well as a hearing Dutch person would understand spoken English if they had never learned it, that is, not at all, unless they have studied it.
If you are living in the Netherlands and want to communicate with local deaf people, learning NGT is the practical choice. NGT has its own online resources, courses, and dictionaries (e.g., from the Dutch Sign Centre or local organizations). ASL is useful if you plan to move to the US or Canada, but it will not help you in daily life in the Netherlands. Many online resources for ASL are indeed abundant, but that does not make it a substitute for the local sign language.
A realistic next step: decide where you will primarily interact with deaf people. If it is in the Netherlands, start with NGT. You can find free online NGT dictionaries and paid courses through Dutch educational platforms or community centers. If you truly plan to move around to many countries, note that sign languages are not universal, each country has its own. ASL is only one of many. Learning ASL first might give you a base, but you would still need to learn NGT from scratch to communicate here. A better approach might be to learn NGT now and then later learn ASL if needed, as many sign language skills (like visual grammar and handshape dexterity) transfer.
In short: for local use, learn NGT. For international travel, ASL is helpful but not a shortcut in the Netherlands. Be honest about your goals and invest in the language that matches your actual community.