Can session persistence time impact load balancing

What do you mean by service is stopped? Do you mean stopping pool member service and making it unavailable?

Coming to your query - Can session persistence time impact load balancing ?

My answer would be YES. With persistence profile, you might see uneven load balancing on the pool members. Because, due to persistence client will connect to the server to which they had connected last time if persistence table has its entry.
Persistence entry will be maintained until its time out/expiry.

If member becomes unavailable, the persistence entries will be still there until it gets timed out or expired, and it will be used if it is still there and pool member becomes available before entry is expired. 
When pool member is unavailable and a connection matches an entry in the persistence table for same unavailable pool member, this entry will be ignored as pool member is unavailable and the new connection will be made with available pool member based on the load balancing method. With this, new persistence entry will be added in the persistence table.

Feel free to ask if you still have any queries.

Hope it helps!