No, this sentence is incorrect. You need each item in the list to start with the same format. Here is one re-writing using "to":
"Is the purpose of this instrument to pull the sheet off the coil, to straighten the sheet, or to guide the sheet through the rest of the machine?"
Here is another example, using the gerund "ing" form:
"Is the main purpose of the instrument pulling the sheet off the coil, straightening the sheet, or guiding the sheet through the rest of the machine?"