I think you do. You hope for an effectual outcome, an effectual wooing. Therefore, you pray hoping for an effectual "drawing".
Or would you actually say you hope God does what he says he will do (as you believe) and draw everyone? If so, then you have the same predicament as the Calvie... why pray for something God said he would do already. Unless, you are hoping for an effectual drawing, thus the purpose behind the prayer. That is the only thing that makes sense.
Non-Cals do not believe in your "effectual" calling, although we do believe God knows best how to influence a person. A good example is Jonah, God knew exactly how to persuade him to go to Nineveh.
I believe God calls and draws everyone, but at some point God will give "up" or "over" a person to a reprobate mind. I pray God would not give up on this person and continue to draw and call them.
You see this in the Bible, when the Jews sinned God was going to destroy them, but Moses prayed that God would forgive them.
Num 14:11 And the LORD said unto Moses, How long will this people provoke me? and how long will it be ere they believe me, for all the signs which I have shewed among them?
12 I will smite them with the pestilence, and disinherit them, and will make of thee a greater nation and mightier than they.
13 And Moses said unto the LORD, Then the Egyptians shall hear it, (for thou broughtest up this people in thy might from among them; )
14 And they will tell it to the inhabitants of this land: for they have heard that thou LORD art among this people, that thou LORD art seen face to face, and that thy cloud standeth over them, and that thou goest before them, by day time in a pillar of a cloud, and in a pillar of fire by night.
15 Now if thou shalt kill all this people as one man, then the nations which have heard the fame of thee will speak, saying,
16 Because the LORD was not able to bring this people into the land which he sware unto them, therefore he hath slain them in the wilderness.
17 And now, I beseech thee, let the power of my Lord be great, according as thou hast spoken, saying,
18 The LORD is longsuffering, and of great mercy, forgiving iniquity and transgression, and by no means clearing the guilty, visiting the iniquity of the fathers upon the children unto the third and fourth generation.
19 Pardon, I beseech thee, the iniquity of this people according unto the greatness of thy mercy, and as thou hast forgiven this people, from Egypt even until now.
20 And the LORD said, I have pardoned according to thy word:
God was pretty fed up with the Jews here, and was going to destroy them. But Moses made a very persuasive argument, that God himself would be dishonored if he destroyed the Jews, and that it would be said that God was not able to bring his people into the land he swore he would give them.
God listened to this argument and granted Moses request.
This just shows that all things are not pre-determined, that God hears prayer, and that prayer can change things.
All this would be nonsensical if Calvinism is true.