Draw a Card vs. Remove a Card

[Zanmor]

I'm working on a deck that uses Parallel Thoughts (http://www.mtgvault.com/ViewCard_Popup.aspx?CardName=Parallel%20Thoughts&Edition=SCG&Print=1) to set aside the high mana cost cards before playing Undying Flames (http://www.mtgvault.com/ViewCard_Popup.aspx?CardName=Undying%20Flames&Edition=SOK&Print=1) for the big kill shots.

Undying Flames states, "Remove cards from the top of your library from the game until you remove a nonland card."

And Parallel Thoughts says, "When Parallel Thoughts comes into play, search your library for seven cards, remove them from the game in a face-down pile, and shuffle that pile. Then shuffle your library. If you would draw a card, you may instead put the top card of the pile you removed into your hand."

So does the wording of UF prevent me from drawing from the pile, or is 'removing cards from your library' equivalent to drawing cards?

[rileyandholly88]

I'm working on a deck that uses Parallel Thoughts (http://www.mtgvault.com/ViewCard_Popup.aspx?CardName=Parallel%20Thoughts&Edition=SCG&Print=1) to set aside the high mana cost cards before playing Undying Flames (http://www.mtgvault.com/ViewCard_Popup.aspx?CardName=Undying%20Flames&Edition=SOK&Print=1) for the big kill shots.

Undying Flames states, "Remove cards from the top of your library from the game until you remove a nonland card."

And Parallel Thoughts says, "When Parallel Thoughts comes into play, search your library for seven cards, remove them from the game in a face-down pile, and shuffle that pile. Then shuffle your library. If you would draw a card, you may instead put the top card of the pile you removed into your hand."

So does the wording of UF prevent me from drawing from the pile, or is 'removing cards from your library' equivalent to drawing cards?
The pile removed is not your Library. Your Library is the original deck you began with, so your combination wouldn't work. Creative though.

[Shadowex3]

The real trick to Undying Flames is using it in a farmville deck that also runs a few eldrazi spells or similar.