To be able to crop the equivalent of a 2X teleconverter you would need a camera with 4X the pixels: twice as many both vertically and horizontally. With twice the pixels using the D7100, you can crop to the equivalent of a 1.4X teleconverter + D300 and wind up with the same number of pixels.
Another answer already covers the theoretical side very well, so we'll talk about the practical side here.
Most of the time when you see similar questions it is posed with assumption the camera body will remain the same and the comparison is either cropping vs. a teleconverter or longer lens vs. teleconverter. In most comparisons I have read that did fairly objective testing, the high quality teleconverter won out over the same lens + same body + cropping. But usually not by a lot. Although it reviews Canon extenders rather than Nikon, here is one such comparison.
By throwing a different body into the mix, it alters the parameters. The D7100 has roughly twice the pixels of the D300. The pixel pitch for each camera is 3.9µm vs. 5.4µm (Hmm... there's that 1.4 ratio again). I would expect that will make enough of a difference to push the quality (in terms of acutance) of a D7100 cropped to 3018x2010 (6MP) to that of the D300 with a 2X convertor unless the final viewing size is large enough to reveal the lower resolution. You would additionally gain the advantage of not having to deal with the drawbacks of a teleconverter: Loss of two f-stops of light at the time you are shooting, decreased contrast, loss of edge sharpness, additional vignetting, etc.
In terms of comparing the D7100 to the D300:
- You gain two stops of ISO on the high end and one on the low end. The native sensitivity of the D300 is ISO 200. ISO 100 on the D300 is ISO 200 divided by 2 (with no increase in S/N ratio, dynamic range, etc). ISO 200 on both cameras is really ISO 145 as measured by DxO Mark. ISO 100 on the D7100 is measured as ISO 69. Both cameras' actual ISO is measured about one half stop less than rated across their entire ISO range.
- S/N ratio is slightly better set at ISO 12800 (21.9db) with the D7100 vs. ISO 6400 (21.1dB) with the D300, so you gain a little more than a usable stop in terms of noise on the high ISO end, and just under a full stop on the low end (D7100 @ ISO 100 = 41.1dB; D300 @ ISO 200 = 36.8dB).
- The D7100 has about 1.5 stops better dynamic range at ISO 200 and moves to a two stop advantage at the high ISO extremes. Again, you gain another stop with ISO 100 on the D7100.
- Tonal range and color sensitivity show similar gains as S/N ratio does with the D7100 vs. the D300.
Here's a link to a comparison of the sensor performance of the D7100 vs. the D300 at DxO Mark. Click on the Measurements tab, then each of the parameters to view a graphic comparison.
Of course the big comparison is this:
- D7100 = $1,200USD
- TC-20E III AF-S 2x = $480USD
The question to be answered thus becomes, "Are the advantages of the D7100 vs. the D300 that you will enjoy with all of your lenses in all of your photography after returning from your trip to Africa worth the extra $720USD?" Assuming you can sell the D300 used for around $500USD, the difference is only about $220USD. In those terms I would opt for the D7100.