My read of it was that since the crew requested a VFR departure, FSS called for their clx, activating their flight plan, making them an IFR aircraft... The original question referred to a class E zone with no FSS (or at least no (R)AAS - ie YGQ), where this could not happen!
From the Designated Airspace Handbook: (bold is mine)
All high level controlled airspace above FL600 within the SCA, NCA and ACA. Also, low level airways, low level fixed RNAV routes, CAEs, Transition Areas or CZs established without an operating control tower may be classified Class E airspace.
A few references from the AIM:
7.9 IFR Departures from Uncontrolled Airports
Where a pilot-in-command intends to take off from an uncontrolled aerodrome, the pilot shall:
1. obtain an ATC clearance if in controlled airspace;
6.2.1 IFR Clearance with VFR Restrictions
6.2.2 VFR Release of an IFR Aircraft
CARS 602.121 (2) No pilot-in-command of an aircraft shall conduct an IFR flight within controlled airspace unless the aircraft is operated in accordance with an air traffic control clearance pursuant to section 602.31.
With all of the above in mind;
If you have filed an IFR flight plan, you are an IFR a/c as far as we are concerned. Nobody calls the ACC to turn you into an IFR a/c. Whether or not you have (or for that matter need) an IFR clx is a different issue. If you depart from controlled airspace you need approval to depart VFR. Controlled does not mean there has to be a tower or FSS on site, it can be through a RAAS. An exception is a place like CYQI, there is nothing onsite other than my frequency but it is class E. So long as it is class E airspace it is controlled. If as you say above, CYGQ is class E, you need approval to depart VFR.
If an a/c calls FSS and requests a VFR departure, FSS calls me to ask. They do not call me for a clx, or to "activate" the flight plan, they are seeking approval for the VFR departure. If I approve it, I specify a time, location or altitude for the a/c to expect an IFR clx. I have, in 20 years, only refused the request once and it was due to workload. The aircraft (an airline) ignored the refusal and departed anyway.
In an earlier response it was mentioned that you can depart on an IFR clx and fly IAW VFR. In this case I would issue a full clx and instruct the a/c to maintain VFR until an altitude, time or location. I have never had a request for this. In both cases the a/c must request it.
If the airport is in uncontrolled airspace you do not need my approval to depart VFR. What you do need is a clx from me to enter controlled airspace. So at places like CYCH, CDT5, CFH4, CYTN etc, while the a/c may call me on the phone for a clx, it isn't unusual for them to depart VFR and immediately call me for a clx. If I'm busy they wait (maintaining VFR). Otherwise they get their clx. In all of these cases you are still being provided alerting services, ie: if we don't hear from you within the specified period of time, we start looking for you (through your dispatch or airport operator etc). If you file from CYCL to CZBF you will not get a clx from me as the entire flight is within uncontrolled airspace. You are still IFR and you will still get alerting services. In this case the a/c calls me to activate the flight plan and has to file an arrival report.
One other type we see daily is the flight between CYHZ and the offshore oil rigs and return. The rigs are in uncontrolled airspace so the a/c never call before departing from them. Their dispatch calls us and lets us know they have departed (alerting service) but that's it. The must get a clx from me before entering controlled airspace south of CYHZ. They are still IFR a/c, they just don't have an IFR clx.
Hopefully I haven't muddied the waters too much with this explanation.