The sentence "could check on this" is correct and usable in written English.
You can use it when you are suggesting an action to somebody. For example, "I'm not sure if I've put the right amount of sugar in this cake - you could check on this before we put it in the oven".
Mr. Sckalor said that he was sold on the clickers because he could check on the progress of every student, not just the ones who frequently raised their hands and tended to dominate the discussions.
If desired, you could check on the progress of your soaked hands every 5 minutes during this process.
Sometimes I kept the television on in the other room, with the sound off, so that I could check on the progress of the race.
In response, the pro-eruv forces created a telephone hot line in Yiddish so families could check on the condition of the enclosure right before the Sabbath began.
Mr. Murtha conferred with the I.N.S. lawyer, and the judge adjourned the case until immigration officials could check on the status of the Ramoutars' green-card application.
She dressed in a T-shirt and jogging bottoms — as if she were someone who took exercise and cared about her health — and then she went to the windowsill so that she could check on the wasps.
If he took the time to take some recent inventory, he could check on the progress of Lee, who was the youngest to win the United States Amateur, at 19, and came into the Masters last year as a "can't-miss kid".
For four days I camped nearby with my Bucknell colleague Beth Capaldi Evans and senior biology major Gemma Dugan so that we could check on the plants each day.
I assumed she planned to grab her cell phone off her desk so that she could check on her loved ones, but I learned later that she was looking to protect different loved ones: her thesis and data.
Motley kept at it, at one point driving to the compensation office in Madison so he could check on his application in person.
The girlfriend said that the police then drove Mr. Scott to his mother's home so they could check on her.
