I need to impedance match an IF mixer circuit to a 10.7MHz crystal filter. One of the inductors was calculated to be 44 $\mu$H. So I need a relatively large value inductance in a small package to fit a small printed circuit board. Is it ok to use a molded choke for this purpose or will the earth stop turning?
In general, a choke would not be a good choice for this type of circuit as explained below. Given the relatively high frequency of your application, I would expect that you could find more suitable values or topologies for your impedance transformation requirement.
Technically, the difference between a choke and an inductor is only a matter of application. A choke is an inductor that is designed to pass DC while blocking RF current. However, from a practical perspective there can be significant differences.
Since a choke is designed to block RF, generally the choke will have a relatively low Q (quality factor). It may consist of many, multi-layer windings using a relatively small gauge wire. With a small diameter wire, the DC is free to use the complete cross section of the wire while the RF cannot due to skin effect. Thus as the frequency increases, the RF sees more series resistance in the inductor which lowers its Q, thus increasing its losses.
Due to the intended application of RF chokes, they are not always temperature stable either. In a critical matching circuit, this could result in a temperature based variation in the transform.
Finally, RF chokes have distributed capacitance that results in a self resonant frequency of the choke. In a critical application such as a tuned circuit, this parasitic capacitance can have a detrimental effect if it is not included in the design model.