Yes and no.
Basically, when you set up a normal domain (we'll call it domain.tld) in Plesk, it configures Apache to respond to requests for pages from domain.tld on certain IP addresses configured withing the panel (e.g. the IP for shared hosting)
When you add a domain alias (alias.tld), it basically does the same thing (and arranges for email sent to alias.tld to go to the corresponding mailboxes at domain.tld, *and copies DNS records*).
So, at this stage, the A record for alias.tld will be pointing to the same server hosting domain.tld, which is no good.
In order to resolve this, you need a way to create an A record in the DNS for alias.tld pointing to the IP address of you Plesk server, not the one hosting domain.com
Now, as you have defined alias.tld as an alias to domain.tld, there is nowhere in Plesk where you can configure the DNS for it separately to domain.tld (but see later).
What you can do, however, is see if the registrar you used to register alias.tld provides DNS record management. If they do, configure your domain to use your registrar's DNS servers instead of pointing to your own (i.e. Plesk), and then adjust the DNS settings as appropriate - most probably idential to those of domain.tld with the exception of the A record (or at any rate the record that eventually points
www.domain.tld) pointing to your Plesk box.
The only other thing I thought of was to create a real account instead of an alias for alias.tld. You'd have to arrange for email to be redirected to domain.tld but if you don't have many accounts then that won't be too difficult.
There may also be a better way of doing all this -- if there is, I'm sure someone will suggest it.
All this assumes your Plesk box acts as the nameserver for your domains. If not then it will be simple to change the records wherever they are for alias.tld.
I'm also assuming that your Plesk box handles the email for domain.tld, which is why you wanted to set up an alias rather than just adding a separate plan/account.