What about Vin < 6V? Truly equal voltages are awfully rare.
(Maybe pedantic, but precision is everything!)
I don't know if your specific regulator will do it, but regulators in general, simply pass input to output when below threshold, and regulate when above.
The catch is: for linear regulators, the drop is the dropout voltage, which varies by type. It can be more-or-less arbitrarily small, given free choice of type.
For buck regulators, often the switch is a high-side N type (NPN/N-ch) supplied from a bootstrap circuit, so its driver depends on the output to be switching constantly, to obtain supply power. These typically have a maximum duty cycle limit, which might be, say, 90% or something. As a result, there's a dropout equal to the same fraction of the supply voltage; rather than a fixed drop (as a linear might have), it's a proportion. So, if the limit is 90% and the regulator setpoint is 6V, an input of 6V would deliver 5.4V, and more than 6.6V input would be required to get the output under regulation.
Some types have drivers that don't require bootstrap power, though the price paid may be notable voltage drop anyway (e.g. a PNP pullup into an NPN follower, dropping about 0.8V), so again having a similar fixed drop to a linear reg. Others use a P-type switch, or an internal charge pump or external bias supply instead of a bootstrap supply, allowing the switch to be held on statically (100% maximum duty) and thus dropping very little voltage in dropout.
Also take note of ULVO / startup voltage, or other enables or faults that may apply. Obviously, the regulator won't operate at all, below its enable threshold. So the transfer curve (Vout vs. Vin) will probably be zero at low voltages, then a step up to the Vout ~= Vin ramp, then as Vin passes Vreg, Vout levels off.
Another good application for this kind of regulator, is as an active current limit. Whereas a linear current limiter device has to dissipate huge power and thus typically can only do so for a short time (say, some ms), a switching regulator can do it for very little loss and therefore a long time (100s ms, or continuously even). Note that you need a current mode regulator of course; this doesn't work with voltage mode. (That's fine, voltage more regulators are awful anyway.)
Tim