My understanding is that there are two broad camps in sufism - 'drunken' and 'sober'. I do not know whether the first term is a description taken directly from the Islamic tradition, I take it to mean Allah-intoxicated. I take the second sense to 'see' Allah through the eyes of the intellect.
Is al-Arabi a sober sufi?
The difference between a drunk and a sober mystic isn't that the former is intoxicated while the latter is intellectual since per definition all mystics (urefa) or in the social term sufis follow the way of the heart. So both the drunk and the sober are intoxicated and driven by the love of Allah; however the difference is in how the love is manifested. For the drunken mystic the intoxication is manifested in acts of love, he goes forth with love and does acts of love. He isn't concerned with the amount of acts but rather the quality of the acts. For example Allamah Tabatabai (a Shia mystic and scholar) used to break his fast during the month of Ramadhan by walking to the sanctuary of Masumah (the sister of Imam Ridha in Qom) and kiss her grave and then head back home to actually eat food. You could say the divine names of beauty is dominating in a drunken mystic.
A sober mystic is one whose love is manifested in obedience. He does acts of obedience and worship and no one is his peer in this regard. Ayatollah Hajj Agha Maliki Tabrizi (another Shia mystic and scholar) is an example of this who with his wailings and long prayers was recognized as Sheikh Munajatian (the sheikh and leader of the invocators). The divine names of majesty are dominating in the sober mystic's heart.
The distinctive characteristic of the late Haji Mirza Ali Agha Qazi was his cheerfulness and faith rather than fear. The same was true of the late Haji Shaykh Muhammad Bahar. On the contrary, the predominant feature of Haji Mirza Jawid Agha Maliki was fear rather than hope and cheerfulness. That is what is indicated by their sayings. According to the gnostic parlance he who is dominated by cheerfulness is called a "drunkard" and he who is dominated by fear is called a "hymist". The best thing is to adopt a middle way in between these two extremes. In other words the devotee should have the highest degree of both the qualities at one and the same time. This degree of excellence is found in the case of the Imams only.
(Source: Allamah Tabatabai, Light Within Me, "Rules of Attaining Spiritual Perfection")
When it comes to Ibn Arabi it appears as if he is more drunk, judging from his texts and biography, albeit he is very balanced compared to many other mystics.
In Arabic drunken interpreted as "sakar" and sober as "sahv". In sakar the sufi is intoxicated in divine love of Allah Almighty and pass the different stages of tasawuf in intoxication, like the chisti sufis are fond of samah(qawali) during samah the chisti sufis are intoxicates and they have no control over themselves. The sufis of other salasil espacially naqshbandi and qadri are againt sakar and they are sahvi they said that to find the true path to Allah and to see Him you always have to in full senses. Answer of second question, No prophet no sufi can see Allah Almighty with the physical eyes its only the greatness of Holy Prophet Muhammad sallala ho aliahi wasalum. He is the only one who saw the Allah Almighty with physical eyes. Sufis do mushahida(vision) of Allah Almighty in dreams or in condition of sakr(drunkness/intoxication). Ibne Arabi was drunken(sakari) sufi.
