Map Windows SMB shares via Profile Manager?

This is a standard option in Profile Manager, try the following.

1. Login to Profile Manager as your admin account
2. Go to the device/user or group you are using for defining settings
3. Select the Login Items payload
4. In Login Items scroll down to Authenticated Network Mounts
5. Click the + symbol
6. Change the protocol to SMB
7. Fill in the host name e.g. server.domain.com and share name e.g. Files

When the user logs in to their Mac it will automatically use their username and password to try logging in to that share. This means the user account needs to be either a network login account or a portable home directory account. A purely local account it not linked to an Open Directory or Active Directory account and hence will not work.

If your using a server name like 'fred' so that the URL is like smb://fred/sharename then this is not ideal. It relies on Bonjour working or a search domain being defined in your network settings. So smb://fred/sharename might get translated to smb://fred.local/sharename

You will notice I suggested previous as an example server.domain.com not as apparently you have tried just server

Some networks especially some Windows networks may have historically hijacked the use of .local for Active Directory which can seriously interfere with its use by Bonjour.

Do you or could you use a 'proper' style domain? Even a fictitious one like mydomain.private with therefore a server as fred.mydomain.private would be preferable.

(As far as I am aware no one has officially registered the domain .private and is unlikely to do so.)

The fact you are using Profile Manager implies you may have a 'proper' domain name in use on your network which you could try.

Yep it looks like the problem is down to hijacking Bonjour.

Maybe the simplest option is to just the static IP address e.g. smb://192.168.1.12/sharename

Less than ideal but if you are stuck with your AD using .local it might be the lesser of two evils.