Yes it will drop existing primary key. You can try like below
DROP TABLE IF EXISTS test_index;
Query OK, 0 rows affected (0.04 sec)
CREATE TABLE test_index(ID INT , PRIMARY KEY(ID));
Query OK, 0 rows affected (0.25 sec)
ALTER TABLE test_index ADD COLUMN email CHAR(50) NOT NULL;
Query OK, 0 rows affected (0.33 sec)
Records: 0 Duplicates: 0 Warnings: 0
ALTER TABLE test_index DROP PRIMARY KEY , ADD UNIQUE KEY (ID) , ADD PRIMARY KEY(email);
Query OK, 0 rows affected (0.48 sec)
Records: 0 Duplicates: 0 Warnings: 0
show create table test_index\G
*************************** 1. row ***************************
Table: test_index
Create Table: CREATE TABLE `test_index` (
`ID` int(11) NOT NULL DEFAULT '0',
`email` char(50) NOT NULL,
PRIMARY KEY (`email`),
UNIQUE KEY `ID` (`ID`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8
1 row in set (0.00 sec)