SRAM HM6264 chip write cycle while output enabled (OE low fixed)
\$WE/\$ turns off the output drivers during the write cycle so no it does not write it's own data.

HOWEVER, when driving the chip in this mode, you need to drop \$WE/\$ before you apply the write data to the data pins. Data should not be driven onto the bus from the writer till after \$T_{whz}\$ later. Further, when \$WE/\$ is brought high you must remove your driving data before \$T_{oz}\$ time expires but not before \$T_{DH}\$ expires.

Unless there is a pressing reason not to use \$OE/\$ I strongly suggest you use it.