How will the connection of the basement to the central heating affect the radiators?

Good afternoon, Alexey. Depends on the area of ​​the basement and the number of connected radiators. It is impossible to give an exact answer without input data. Properly connected to the circuit, in principle, is possible.

Please note that the insert without coordination is fraught with consequences. Open the Housing Code, Article 29 - “Consequences of unauthorized conversion and (or) unauthorized redevelopment of a dwelling”.

See item 1: “Unauthorized are the reorganization and (or) redevelopment of a dwelling, carried out in the absence of the basis provided for in paragraph 6 of Article 26 of this Code, or in violation of the project of reconstruction and (or) redevelopment submitted in accordance with clause 3 of part 2 of Article 26 of this Code.“.

And immediately point 3: “The owner of a dwelling that has been arbitrarily rearranged and (or) re-planned, or the tenant of such a dwelling under a social contract of employment, is obliged to bring such a dwelling into its former state within a reasonable time and in the manner established by the body that carries out the coordination.“.

Also look at the question from an ethical point of view. Most likely, a heat meter is installed on the house, monthly the cost of heating 1 m2 is calculated according to the consumed gigacalories. It turns out the heating of your basement will be paid by all residents of the house.