Yes You can either create a Selectable input fields for users to select their user type to register.
You can also create different pages for registration of different user types.
First of all create user levels you require by going to User levels add new. And make sure you name them without space and you provide redirect file URL also so when a user of that type login they can redirect to that user level.
Then go to General Settings and select default site's user registration type. General settings can be accessed by clicking your icon above right and clicking on that icon.
Now edit or copy register.php find following lines
<!--Default register user is subscriber, you can change it to any other level you have created-->
<input type="hidden" name="user_type" value="subscriber">
You can change the value of this field to your desired user level. Also you can make it as selectable dropdown.
Remember this way you cannot register a admin user level.
To use selectable field in same user level file.
<select name="user_type">
<option value="subscriber">Subscriber</option>
<option value="customer">Customer</option>
<option value="crew">Crew</option>
</select>