Yes, you should check that box because it is a nonstandard W-2 form with any hand written information. The IRS would expect you to indicate the W-2 is nonstandard. They require the question in the software if any company wants to have IRS approval for e-file.
A non-standard W2 does include handwritten, typewritten or a W2 that is changed in any way.
When entering your W-2 information in TurboTax, the program will ask you if you have any "Uncommon situations" - such as Non-standard W-2, which you have. Indicate yes - If the program directs you to complete form 4852, please do so. (Not always needed since you are have all the data from your W-2).