Yes, I would understand it and that’s probably what people naturally say informally where I live in Scotland and in other dialects it’s said more like ‘go’n put your shoes on’ where the ‘n’ is very soft. But especially if I saw it in writing I would assume that they were not a native British English speaker. It’s interesting. In America I presume it’s not grammatically correct to say ‘the police officer went got his gun and shot killed the suspect’ so why does US English drop the ‘and’ from go (and) or try (and)? Curious. (Edit with some observations about dropping letters from and)

'Go put your shoes on' is just another slightly different example of pseudo-coordination. I'm guessing that is has various levels of acceptance per-dialect (even within the UK) just like 'try and'.