Will you get a positive hpt at any point in your pregnancy if you're pregnant?

Yes. Unless the test is defective or the patient is not pregnant the "hpt" pregnancy test will be positive. Unless I am misunderstanding your question?! this abbreviation is not commonly used here in the us. This is a repeated question.
No. A home pregnancy test is usually positive no earlier than 10 to 12 days after conception. Sometimes if the test is not very sensitive then it may take up to 14 days after ovulation.
Yes. Hpts measure urine HCG levels, which peak early but are present during pregnancy and after delivery. If any confusion, do a blood HCG test.