This is entirely consistent with accepted accounting practice, using a technique known as group accounting - which produces consolidated financial statements (income, balance and cash) amongst a related group of entities. The international accounting standard for that is IFRS 10 'Consolidated Financial Statements' which requires that entities under common control present a consolidated set of accounts so that external users can obtain a 'true and fair view' of the actual underlying economic transactions.
The Central Bank in all sovereign jurisdictions falls under the definition of control by the Treasury - often de facto by the operation of law (Bernanke: "Our job is to do what Treasury tells us to do"), but also de jure, e.g in the Sterling area HM Treasury actually owns the entire shareholding of the Bank of England. The control model in IFRS 10 is elaborate to try and catch all those little tricks that entities use to avoid having to consolidate accounts and is worth studying to see the various 'Wizard of Oz' methods that control can be imparted even though the public face is supposedly independent.
Given the control relationship, consolidated financial statements are entirely appropriate and correct accounting which reveals the essence of the underlying transactions. Therefore in your model you should be able to swap out the detailed entities and replace them with the consolidated entity and nothing about the response should change. If it does then it is likely your model is wrong.
In Information Systems this is known as white box and black box testing. With white box you can see the internals and with black box you can't - requiring you to conform to that modules interface in your testing.
So let's look at the white box of the UK government sector
the current operations document at the Bank of England, HM Treasury's remit to the Debt Management Office but also this rather nice description of the Central government spending flows which has a very useful picture in it:
Importantly what this arrangement of accounts tells you, along with the description of the way Reserve accounts work at the Bank of England, is that spending is disconnected from the debt management operation. All entities operating at the Bank of England have an interest free overdraft available during the day to absorb flow differentials, and this effectively means that they spend on their accounts and then back fill (or under fill) to the target account balance using standard asset and liability optimisation mechanisms.
Very likely some of the government spending flow out to the private sector stock accounts earlier in the day will flow back later in the day to the National Loans Fund in exchange for Treasury bills or Gilts as a completely separate transaction. Spending therefore demonstrably comes first. Moreover it is in the Debt Management Office's interest for that to be the case since it ensures there will be healthy demand at the funding auctions.
Once you apply group accounting techniques to the government sector you get the black box view - which is remarkably simple.
All the government sector does is allocate tokens to the non-government sector (often in return for some real provision to the government) and then swaps those tokens around for different tokens which attract different income flows and have different liquidity characteristics and holding criteria. The elements this simplification reveals are quite interesting. For example, if I have a young child and qualify, then that child attracts Child Benefit. If I then sell that child to the gypsies, then the gypsies start getting the Child Benefit instead. There is remarkably little difference between a Gilt and a child from the financial systems point of view - a difference in the income stream attached and a difference in liquidity, holding cost, collateral value and issuing criteria :)
With this model you can see that QE is a token exchange - Gilts for Bank Reserves. The income flow goes down - because entities holding Bank Reserves receive less government spending than entities holding Gilts. So you will get a portfolio reconfiguration - since there is less income to go around and the mix of tokens has changed. Bank Reserves have a narrow holding criteria than Gilts and therefore are likely to create offsetting commercial bank deposits that have a wider holding criteria.
The detail is important to understand how the government sector works internally and to understand the actual operations. But it is very easy to end up in a situation where you struggle to see the wood for the trees. Hence why the consolidated government sector is an important modelling tool.