For all design contests except Logo contests: Yes. But you must declare them and check the license.
Usage of all stock art or royalty free designs (including images, brushes, and patterns) must be reported to the employer along with the source URLs. You must first check the license for all stock images you use to ensure that the image can be used legally as the contest holder intends.
If there is a cost associated the use of stock designs or tools, the designer is responsible for reporting this to the employer. You can report the information when you submit your entry.
For Logo contests: No. Even if YOU designed them and posted to a stock image/clipart site before the contest.
All logo designs must be 100% original and cannot use any stock photos, images or clipart (such as iStockphoto), even if they are copyright free.
Furthermore, you may not use design elements in your logo entries that you have created and uploaded to a third party stock image/clipart site prior to participating in the contest; we promise our contest holders that they will have exclusive rights over the winning design at the end of the contest when they receive the transfer of ownership rights agreement.
If a contest holder’s winning logo contains design elements that were previously posted to a royalty free site, for example, and licensed out to other people, they would not have exclusive rights/use of the design; the contest holder might have trouble trademarking their company logo in the future because others may be using part of their logo for commercial purposes.
Failure to comply to this policy will result in serious consequences, which includes being suspended or permanently banned.
If you wish to report a stock art violation in a logo project, please read this article on How to report a copied design.