AFAIK girls can park their AW profiles if they are taking some time off. Is there any way to know if a profile is indeed parked or if it's deleted?
Yes, there is.
If a girl "deactivates" her profile, no information about her remains available. Feedback she has left for you will no longer be accompanied by her name, but instead by "Member not active". And if you have e-mailed her in the past and now try again, you will get the message, "This member is no longer valid for e-mailing".
For one month after removal the girl can reactivate her profile. After one month, the profile is lost for ever.
If a girl wants her profile to become invisible, but to remain available to be brought back to life if required – at any time, even years afterwards – she will change "Offering services" to "Seeking services" on the Registration page.
If she has done this, her feedback will continue to appear under her own name and you will still be able to e-mail her if you haven't deleted previous e-mails to or from her. (In other words, her Adult Work "name" will need to be available in your e-mail boxes, so you can click on it in order to e-mail.)
In summary, the simplest way to find out whether a profile has been "parked" or "deleted" – to use the OP's terms – is to click on her AW name in one of your e-mail boxes and see whether you get a blank-e-mail form or the "no longer valid for e-mailing" message.