Voltage Controlled-Phase Shifting Circuits
TL;DR the part you've linked to is suitable for whatever you want, if you're working in the 1.7 to 2.7GHz region.

Figure 6 of the data sheet shows this



For the higher voltages, at constant control voltage, the phase shift with frequency is flat (to my eye) over a 1GHz bandwidth, so is acting like a length of cable. For the lower voltages, I can see a few degrees of bend over that bandwidth, so it's a bit more dispersive than cable. Microstrip is weakly dispersive, though I don't know whether more or less than these low voltage curves. An FM signal covering a 1GHz bandwidth at only 2ish GHz would be quite some signal! For any lesser bandwidth, 100MHz or so, you could call this as flat as cable at all voltages.

For the higher voltages, the phase shift with voltage is slightly greater at high frequencies. For the lower voltages, the phase shift with voltage is less at high frequencies. Between 7v and 8v (by my eye) it appears that the change of phase with voltage is essentially independent of frequency over the 1GHz bandwidth. Again, over a more reasonable bandwidth like 100MHz, it's effectively flat at all control voltages.