No
slackware does not add a .bashrc file by default in install, you have to add it yourself.
Frankly I doubt that source a .bashrc file will fix it, I never used at to open a text editor but if you want absolutly achieve this, you may create a bash script that open pico like :
#!/bin/bash
export TERM=linux
tty=`tty`
pico 1> $tty
then save it as startpico.sh for example and try :
at 20:00
at > /path/to/startpico.sh
at > <EOT>