There are some safeguards in pt-online-schema-change tool to avoid incurring huge slave lags. You can use either of these options:
–max-lag
type: time; default: 1s
Pause the data copy until all replicas lag is less than this value. After each data-copy query (each chunk), the tool looks at the replication lag of all replicas to which it connects, using Seconds_Behind_Master.