Yes it is possible. However, your code is incorrect because you are missing the SELECT because your first choice becomes a set of rows (created at runtime). That is, you must specify the SELECT and the fields that you want to receive. The simplest case:
SELECT a.* FROM (SELECT DISTINCT `Fund_ID`, `Fund_Name` FROM `admin` UNION SELECT `Fund_ID`,`Fund_Name` FROM `admin_custom` WHERE `admin_custom`.`user_id` = 361) AS a LEFT JOIN `qt1` ON `qt1`.`Fund ID` = a.`Fund_ID`
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