Do you think it would arouse suspicion if there was only 2 oz in the cup, and none in the toilet?
Nope. Because not everyone has a full bladder upon entering the collection facility. As long as youre able to provide a sufficient amount of urine sample (again, 2 oz) , thats all they are interested in.

I plan on using Ultra Pure, which I heard doesn't have much of a smell to it.
A lack of odor can be exhibited in human urine samples too.

Also, would it be a bad idea to urinate in the toilet?
It wouldnt be if you have enough urine in your bladder to urinate in the toilet.

Could they test the urine that is in the toilet?
Nope, drug tests are not conducted in that manner. Testing costs money and testing facilities, like any other business, have a profit margin to look after. They are not going to imperil their bottom line by running such a test, only to find the sample either "too-diluted" (due to the large amount of water in the toilet bowl), or "adulterated" (due to the bluing agent thats present in the toilet bowl, as required by the regulations outlined by the DHHS).