How can I guess if a USB cable will power my devices?

I find it impossible to believe that USB cable can't supply enough current for a device and that for power supply use length of SUB cable can matter.

Here's some reasoning why:

I'll cite USB specification 2.0. It says that the minimum cable which may be used for USB is AWG 24 cable. If we say that the device has 10% voltage tolerance, it'll need at least 4.5 V to function. Let's calculate how much resistance we need for such voltage drop. Maximum current consumption for USB 2.0 is 500 mA. So 4.5 V/0.5 A = 9 Ω. That resistance is quite big for simple cable. Let's take a look at typical resistances of AWG wires. It is said here that AWG 28 resistance is 0.0764 Ω/′.

So 9 Ω/0.0764 = 117,80 ′ which is around 35.9 m.

There are several other reasons why it would work with external power and other cables but not that cable. First thing which comes to mind is timing. Maximum length of USB 1.1 cable was 3 m and for USB 2.0 it's 5 m. The lengths are limited by signal propagation. But you said that if you connect power source to the device, it works. So while we are close to maximum length for signal problems, we aren't in the critical region yet.

This is the point where the problem becomes really complicated as there are lots of variables which could be causing problems. First thing that now comes to my mind would be bad USB chips at drive or motherboard side or both. Also, it is interesting to know that drive has a power source connector. It could happen for example that chip used at the drive can't handle delays caused by the cable if the load is high enough. When the adapter is used, there could be another power supply inside the drive which powers the chip.

On the other hand, it could happen that the motherboard itself isn't providing clean enough power. In that case voltage could be carrying some signal which could interfere with data lines. Length of the cable could make interference worse. It could also happen that signal source shows only when the load is high enough.

Basically, form this point on, it's mainly guesswork, because there could be combinations of bad chips at both sides, bad shielding in the cable, bad filtering and so on. To sole such problems, large amount of knowledge would be required about internal construction of the motherboard, hard disk and of course, there's the test equipment.

To answer your question directly, you can't know in advance if a cable and adapters will work correctly with a particular combination of devices, so the answer is no.

Unless it is a really low quality cable, your voltage drops are most likely to be caused by the connections. Using adapters could make it worse.

If this is a PC with a front panel USB connector, it would be worth checking to make sure that you have a good connection at the mother board end of the front panel lead. As the current drawn through the cable increases, so the voltage drop across any poor connections increases, so your cable may not be able to provide the correct voltage for the HDD.

Signal lines, however, don't draw a lot of current, so the voltage drop could be insufficient to affect the logic levels involved.