This has been an approach I've seen used to great effect by people learning your language! My wife strings together Dutch words with English grammar (we're both American) and it's a common "mistake" that I experience when visiting a taalcafe.
Our brains are all extremely capable of moving a few words so we can understand things in context. When speaking Dutch, I'm spending a lot of time thinking about a verb, then attempting to string it together into something comprehensible.
What I also found to be almost universally true, is that if you are learning a less "popular" language (like Dutch or Ukrainian), just actually give a shit enough to learn more than "yes/no/please/thank you/my name is" will garner you a lot of good will from native speakers. Some countries get so many tourists that hearing the same 10 words butchered over and over and over and over and over again eventually starts to wear down on locals, making them jaded.
When you can walk into a room and somewhat confidently hold your ground, you become interesting and a novelty that people want to interact with. I went to a block party last weekend and spoke to most of the people there throughout the evening. Sure, everyone knew I was "foreign" and occasionally I had to ask someone to repeat something or re-word it, but that's a minor complaint for them considering the other option is to speak back to me in a language they don't have as good of control over. Despite popular belief, even in many "English friendly" countries, the normal citizens aren't actually that comfortable speaking unless they work in an environment that demands they speak English every day. This goes doubly so for older people. My next door neighbor is about 75 years old and speaks English pretty well (worked at Philips for 20+ years), but the _quality_ of our conversations went up 3x when I could understand enough Dutch for them to speak naturally to me.
All that to say, I agree with you! Vocabulary and basic grammar to get you started and then after that it's all about learning words and practice practice practice.