If the controller is following FLAS - Flight Level Allocation Scheme, which permits the level, then there's no "loss of separation". FLAS typically takes the form of a diagram or table of the FL's that are allowed in a certain FIR or airspace and also the restrictions on direction, and sometimes further restrictions such as timings or Metric level values etc. It lays down exactly which levels are allowed, in which direction etc. rather than using only a description or formula such as "2000 ft separation". You can check your FL in the table, see what it says, and plan or base your tactical request accordingly.
Here's an example from the UK Flight Planning Guide, CAP 694.
OTS above refers to the Organized Track System in special airspace NAT HLA (earlier MNPSA), ie crossing the Atlantic.
Note also that FL430 is 'traditionally' an eastbound level, but as you can see, this has been modified under FLAS
Here's another 'circular' from the AFI (Africa/ Indian Ocean) area that is quite well aligned with the question we're trying to answer.
RVSM FLIGHT LEVEL ALLOCATION SCHEME (FLAS) FL290 TO FL410 AND THE ALLOCATION OF FL420
The application of the RVSM FLAS in AFI is restricted to FL290 – FL410 inclusive for all eligible aircraft.
The application of RVSM is adequately documented in ICAO Document 9574, Manual on Vertical Separation Minimum between FL 290 and FL 410 Inclusive.
It has been observed, during the scrutiny of Air Traffic Flow Data, that FL420 is being allocated.
It should be recalled that the application of 1000FT vertical separation above FL290 is only applicable between FL290 and FL410 inclusive. The next available flight level above FL410 is FL430 and not FL420. 2000FT vertical separation is applicable above FL410 due to altimetry system inaccuracies.
In the event that two aircraft cross each other, one at FL410 and the other at FL420, a reduction in vertical separation is deemed to have occurred. This event will thus pose a risk to RVSM and en- route safety.
Air Navigation Service Providers and Aircraft Operators must ensure that FL420 is not allocated or utilised.
Further to this the allocation and use of FL420 should be immediately brought to the attention of ARMA for discussion with the relevant parties.
RVSM and en-route safety is of paramount importance.
This is also the end of my answer, but I'm leaving in place the previous write up which is quite accurate except that it did not answer the question asked as I misunderstood the question. I regret the error. (The moderator may feel quite free to remove the portion below the dashed line.)
Apart from the vertical (flight-level), the required separation can also be taken care of in the lateral (cross-track to the left or right), and longitudinal (along-track, going relatively faster or slower, to achieve the needful) and ATC uses these to ensure separation before clearing the climb within, or through RSVM airspace. Depending on the type of facilities/airspace, ATC may use Radar Control or Procedural Control (position reports) to achieve this.
At no time would ATC compromise separation or have 'doubtful' separation. RVSM based separation would be applied to RVSM capable aircraft, and non-RVSM separation between any non-RVSM aircraft (or one that has become incapable of meeting RVSM requirements)
If, as in the example the two are close proximity same direction traffic such clearance will not be given except as described above.
If the request is made in good time, or planned ahead (even in the filed plan), it is more likely that you will get the level without undue delay. Though RVSM was introduced to accommodate more traffic, nevertheless, every possible airway/airspace slot is not necessarily occupied and ATC generally try and make the most efficient use of the airspace so as to accommodate flights as planned, as well as accommodate tactical real time requests. Fuel saving is the usual benefit and reducing the aviation's carbon footprint is in everyones interest so there is no prohibition on requesting climbs.
Such clearances to climb or descend may typically have a restriction reach the cleared level "by time HHmm", or "best ROC/minimum Vertical Spd XXXXfpm" or AT a WPT or crossing a Longitude or at a distance X nm from some reference point and once accepted it is the crew's responsibility to ensure compliance of the instructions.
(will try and include suitable references soon, meanwhile @dawg has given a link above)