The answer to this question depends entirely on the use and meaning of the word pray.
If one is referring to the act of making requests or other silent beseeching to a personal deity, then the answer is no. If someone is asking a deity to make their sick friends get well, win the lottery, or help find their car keys then they are theistic. Atheists lack a belief in a deity so they would not pray to one or ask any deity for special favors.
Another use for pray is not used very often these days and is often thought of as purely Shakespearean. Pray can also mean to make a fervent request, entreaty or to beseech someone (ask imploringly). For example your friend has given you a teaser about something that happened to him today and you replay, “Pray, tell!” Not many people still use it – but it is, nonetheless, prayer in the sense of begging someone to fulfill your wish – the praying or beseeching just happens to be to someone or something other than a deity.
Other people use prayer more generically to encompass all forms of entreaty – regardless of the object, person, or supernatural being that one is beseeching. This means we consider some forms of meditation to be prayer.
Some people pray to crystals and believe in sending ‘positive vibes’ through the air with the power of crystals. These people, often called New Age or Neo-mysticism (often unflatteringly called “crystal-huggers”), are technically atheists because they lack a belief in a deity. Since the chanting to a crystal for ‘positive vibes’ is a form of prayer and the chanters are technically atheists, then you can say that some atheists do pray.
Most Buddhists do not view Buddha as a god, but as a prophet or great teacher. Buddhism is an atheistic religion that involves many prayers or meditations and incantations. Buddhists that have not elevated Buddha to godhood (some sects have) are atheists. So again, you can say that some atheists do pray.
Many atheists enjoy the earth-based rituals of the pagan and shaman style religions. They do not believe in the deities of those religions but love the ceremonies, rites, and rituals. We refer to these atheists as Humanist Pagans or Secular Pagans and a large proportion of them are environmental activists (often unflatteringly called “tree huggers”). They participate in the chants, prayers and rites – but only for the ceremony of it. So again, you can say that some atheists do pray.
Some atheists pray and some atheists do not. Of course, the answer hinges on the definition and use of the word pray.