if there is no mirroring configured on VIP level then it will depend on the service.
You may get some short term outage for long lived connection until the connection being reestablished with active bigip.
for short lived connection like http, smtp etc you may even not notice any issue unless you are using sort authentication etc you may be asked to login again.
Actually this is totally depend on your network and service configuration.
In case if you have mirror enabled for vip and persistence (if any) then there should not be an issue.