Are these garden path sentences grammatically correct?

Here is how the example sentences are grammatical:

• The old man the boats.
  The old [people] [man/serve on] the boats

• While Anna dressed the baby spit up on the bed.
  While Anna [got] dressed, the baby spit up on the bed.

• The man returned to his house was happy.
  The man [who was returned to his house] was happy.

• Fat people eat accumulates.
  [The fat that people eat] accumulates

• She told me a little white lie will come back to haunt me.
  She told me [that] [a little white lie will come back to haunt me].

• We painted the wall with cracks.
  We painted the wall [that has] cracks.

One of your examples is punctuated idiosyncratically:

While Anna dressed the baby spit up on the bed.

I've always been taught and I've always taught that adverbial clauses starting a sentence need to be followed by a comma:

While Anna dressed, the baby spit up on the bed.

This isn't mere disambiguation. Rather, the comma grants that clause -- "While Anna dressed" -- its capacity to modify the verb in the independent clause "the baby spit up on the bed." It's the grammatical way of saying, When did the spitting happen, you ask? Well let me give you something to modify that verb. Omitting the comma signals that "While Anna..." will be a noun clause: "While Anna dressed the baby [...was when the doorbell rang]." In this one case, the reeling "garden path" feeling of realizing that the verb "spit" doesn't fit with the noun phrase in front of it is legitimate and caused not by the reader's hasty assumptions but by punctuation that is grammatically uncommon.

Your other examples, though, are wonderful, as they play on grammatically common patterns formed with unexpected combinations.

All the sentences are grammatically correct, including your own.

You could make the meaning clearer by adding punctuation, but this might spoil the fun. For example:

The men, run through the arches, screamed.

I think you are missing something very important here: you're not using any punctuation at all, and that can make a big difference. If you write "While Anna dressed the baby spit up on the bed." your sentence is confusing, but if you write "While Anna dressed, the baby spit up on the bed." with a comma after "dressed", then it becomes an easy to undestand and correct sentence. Punctuation is important for grammar, so, if you don't use any punctuation in your sentences, they're gramatically wrong. There are no difficult to understand sentences, there are only wrongly written sentences.