If your teammate is banned for anything other than the following:
- Cheating
- Illegal Customization
- Ban Evasion
- Payment Fraud
- Malicious Activity
- Karma Threshold
- Account Sharing
- Unsportsmanlike Conduct
- ESIC Enforcement
- Gambling Violation
- Discrimination
- Threatening
Then your teammate will be able to open the ESEA Client and join the league server with no issues. The only bans that prevent this are the far more serious bans listed above.