我认为如果
Call_To_Database_NotAsync 或服务器端函数不支持多个并行执行，因此可以观察到不良影响。找到一种方法来取消过时的请求。

button1.KeyDown+=async(o,n)=>
{
//This is a search function, the user will type something on 
// a textbox then in every keypress, the application will connect
//to the database and search if the typed data has been found 
//then bind it to a gridcontrol
 var getData=Task.Run(()=> Call_To_Database_NotAsync);
 var result=await getData;
 gridcontrol.Datasource=result;
}

Is there a possibility that the grid control will contain no data at all when the user types fast and the connection to the database is slow?

Regards

I think that if Call_To_Database_NotAsync or server-side functions are not designed to support multiple parallel executions, then it is possible to observe undesirable effects. Find a way to cancel the requests that are obsolete.