Latin American Spanish in Spain?
Do the people of Spain understand or even speak the Latin-American style Spanish? For example, here we are taught 'ustedes' but in Spain they use 'Vosotros' instead. These are entirely two different concepts.
You are greatly exaggerating the differences. Both places use ustedes. To ask if Spaniards can understand Chileans is like asking if people from Texas can understand people from Boston.
Can people from Texas understand people from Boston? If so you should use more international analogy such as 'To ask if Spaniards can understand Chileans is like asking if people from Britain can understand people from America.
They're not actually entirely different concepts. They're simply different plural "you"s. Plus, Spain uses "ustedes" as well as "vosotros" - ustedes, like "usted", is more formal, and "vosotros", like "tú", is more informal. Latin America doesn't make that distinction at the plural level and uses "ustedes" for every instance of the plural you.
You can think of it like American English vs British English vs Australian English, etc: It's the same language. There are different accents, some different vocabulary, and maybe a few minor grammatical differences (as an English example - collective nouns are singular in AmE - "the family is nice" - while they're plural in BrE - "the family are nice"). But they are still the same language and people understand each other with perhaps some vocabulary confusion. (Another English example - pavement in the U.S. is what people drive on; pavement in the U.K. is what people walk on, what I would call the 'sidewalk').
They understand, but might comment on it if you use a different mode/dialect then they use. Even the way you pronounce some sounds wil/canl tell people where/from who you learned spanish, but it's not really going to hinder understanding.
Vosotros and ustedes are not different concepts, they mean the same thing and in fact both are used in spain. We latin americans have no troubles whatsoever understanding spaniards and neither do they when it comes to understanding Latin Americans, your question is pretty much like asking if British people even understand people from the U.S or Canada.