Short answer: Yes, changing the word order may lead to a change in meaning.
Longer answer: This phenomenon has to do with the concept of Markiertheit (markedness). Roughly speaking, statements can be expressed in a regular, unmarked form or in a somewhat divergent, marked form. One way to mark a statement is to change the word order. To see this, let's have a look at the following example sentences:
- Die Eltern werden ihrem Kind alles ermöglichen. (unmarked)
- Die Eltern werden alles ihrem Kind ermöglichen. (marked)
- Alles werden die Eltern ihrem Kind ermöglichen. (marked)
- Ihrem Kind alles ermöglichen werden die Eltern. (marked)
The main statements (the denotations) expressed with these sentences are the same. Still, the changed word orders in 2., 3., and 4. are accompanied by a change in sentence stress and thus in meaning: Sentence 2 additionally connotes that it is above all their child who is enabled by the parents (rather than other children or or other persons). Sentence 3 emphasizes that it is all and everything that the parents will enable, adding as a connotation the parents' determination to act. Sentence 4 emphasizes that it is above all the the parents who will enable their child (rather than other people who may also do it).
Addition: A similar question has already been asked a couple of years ago in German, see Wortreihenfolge in »weil du es bist«.