No. The human pregnancy test detects hCG (human chorionic gonadotrophin) which is specifically produced by human pregnancy. Other animals have different hormones that maintain pregnancy, including progesterone (which all female mammals produce at some point in their cycles) among others such as interferon tau. Different hormones can be measured at different times in different species to confirm pregnancy, usually by blood sample. It is particularly difficult to identify pregnancy in dogs for example, because their normal oestrus cycle has very similar levels of progesterone to that maintaining pregnancy throughout, hence why they have a lot of false pregnancies. A blood sample can be used from about halfway through a pregnancy, but I do not believe there is a urine test. There is a urine detection test for pregnancy in mares, but I think it is generally unused, as a blood sample or rectal examination +/- ultrasound is usually easier to get. As far as I am aware, there is also no urine test for cattle, but rectal examination +/- ultrasound is very easy and cheap, and there is a blood sample for bovine pregnancy glycoprotein if inconclusive.
Hope that clears things up for you.