Yes - use TIdHTTP.Head() instead of TIdHTTP.Get(). A HEAD request is identical to a GET request except that no body data is sent, but the response headers will be the same.
A HEAD response will include the 'Content-Length' header, so yes, you can determine the file's size without actually downloading the file.
However, if you are going to download the file anyway then there is really no point in checking for its existence beforehand, just download the file and handle whatever error may arise, such as HTTP 404 when the file does not exist.