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.
[url]pt-online-schema-change — Percona Toolkit Documentation
-check-slave-lag
type: string
Pause the data copy until this replica’s lag is less than --max-lag.
[url]pt-online-schema-change — Percona Toolkit Documentation
The data copy process is performed in small chunks of data and these queries are replicated to slave(s) instantly.