Technically possible? Absolutely: that 30A outlet has two 120V legs, neutral, and earth-ground. So yes, technically possible.

A Good Idea(tm) though? NO. Absolutely not.

The breaker and wiring for the dryer circuit are for 30A. The 120V outlet for the washer will be a 15A (or perhaps 20A) device -- so the available current (30A) would exceed that device's safety rating.

Various electical codes also forbid it -- the washer and dryer, like most permanent appliances, are typically each required to have their own, dedicated circuits.

Cheers