CoinGecko does allow concurrent login from multiple devices per user, be it from your mobile phone, PC, tablet or more!

However, kindly note that users may get rate limited at times when there are a dozen tabs open on the CoinGecko page as this may lead to price feeds on CoinGecko being refreshed automatically. 

Security wise, be sure to logout from your CoinGecko account once you are done browsing on a specific device to ensure healthy security bookkeeping across.