From the picture shown on Hifiberry's site we learn that it uses the PCM5122 Audio Stereo DAC with PCM Interface and Fixed Audio Processing. We also find a RC low pass connected between "something" (traces coming from under the PCM5122 itself) and the audio out RCA connectors. R6, C8 and R3, C7 form these low passes. So the external circuitry does not block DC signals. This circuit might very well be the recommended output filter shown in the datasheet, p. 42 and where we find that:
The PCM512x devices include a two-channel DAC, with single-ended outputs. The full-scale output voltage is 2.1V rms with ground center output. A dc-coupled load is supported in addition to an ac-coupled load, if the load resistance conforms to the specification.
The same document also reads in the feature list (p. 1):
No DC-Blocking Capacitors Required
The PCM512x provides 2.1-V RMS ground-centered outputs, allowing designers to eliminate DC-blocking capacitors on the output, [...]
The datasheet furthermore outlines that the numerous integrated filters have a pass band of 0 to 0.4 (or 0.45) times sampling frequency with zero explicitly included and clearly shown in the frequency vs. amplitude plots.
Bottom line: while I am not sure why one would want to dc couple the audio signal and from theoretical knowledge only (not owning such a DAC+ board) it would seem that this board can in fact output a DC voltage of up to 2.1 V.
Maybe this is more fitting to your needs: Open ILDA DAC board?