Your's is a case of wishful thinking. (Edited for length)
NLRB v. Noel Canning was where I got the idea for this strategy. The court decided that Obama's recess appointments made during pro forma sessions weren't valid because even though the Senate wasn't actually in session, it still had the
ability to conduct business. What drew my eye was the following section from Justice Breyer's opinion:
"...the Senate’s rules make clear that during its pro forma sessions, despite its resolution that it would conduct no business, the Senate retained the power to conduct business. During any pro forma session, the Senate could have conducted business simply by passing a unanimous consent agreement. See Riddick’s 1313. The Senate in fact conducts much of its business through unanimous consent. Id., at 1311–1312. Senate rules presume that a quorum is present unless a present Senator questions it. Id., at 1041–1042. And when the Senate has a quorum, an agreement is unanimously passed if, upon its proposal, no present Senator objects. Id., at 1329–1330. It is consequently unsurprising that the Senate has enacted legislation during pro forma sessions even when it has said that no business will be transacted. Indeed, the Senate passed a bill by unanimous consent during the second pro forma session after its December 17 adjournment. 2011 S. J. 924. And that bill quickly became law. Pub. L. 112–78, 125Stat. 1280."
Since the Senate is technically in session during a pro-forma sitting, according to Senate rules, it had to be assumed that a quorum was present. The Obama Administration's case failed because no Senator actually made a point of order that a quorum wasn't present, and so the Court was forced to assume - according to Senate rules - that a quorum was indeed present and that the Senate retained the ability to do business. So what if a Senator had shown up and made such a motion? Well, according to
Senate Rule VI (3) & (4):
"3. If, at any time during the daily sessions of the Senate, a question shall be raised by any Senator as to the presence of a quorum, the Presiding Officer shall forthwith direct the Secretary to call the roll and shall announce the result, and these proceedings shall be without debate.
"4. Whenever upon such roll call it shall be ascertained that a quorum is not present, a majority of the Senators present may direct the Sergeant at Arms to request, and, when necessary, to compel the attendance of the absent Senators, which order shall be determined without debate; and pending its execution, and until a quorum shall be present, no debate nor motion, except to adjourn, or to recess pursuant to a previous order entered by unanimous consent, shall be in order."
So the motion is privileged, it can be called at any time, and until such point as a quorum can be mustered, the Senate loses the ability to conduct business. What's more, the Noel Canning case also sets out the minimum of 10 calendar days during which the Senate cannot conduct business as the point where the President may then legitimately make recess appointments. The Senate concluded it's regular business and entered pro-forma sittings on Sep. 29. The first scheduled pro forma sitting - presided over by Senator Cassidy - was on Oct. 3 (Day 4). If the Vice President had assumed the chair and the Minority Leader made a point of order that a quorum wasn't present, presumably only Senators Cassidy and Reid would have answered the quorum call. A quorum not being present, the Senate would have had no option but to recess until the next scheduled pro forma sitting.
The second pro forma sitting on Oct. 6 (Day 7) was again presided over by Senator Cassidy. According to Senate rules, the first order of business of this sitting would be an automatic quorum call. At this point, the Republicans would have either had to muster 51 of their 54 members or, again, the Senate would have had to recess without possessing the capability to do business. If they did muster a quorum, the clock starts again at the next pro forma sitting when Senator Reid could have made the same point of order.