Critical oppositions made using inadequate equipment.

+1 @hilde45 - not enough info to draw conclusions

@surfmuz

critically estimate tt or cartridge characteristics

What does “critically” mean? Hearing any changes? If you mean like a professional reviewer then the entire audio chain must be of high enough quality to hear differences. If the later then the answer is no.

cheap monitor speakers

Also vague. Price is not the same as performance.

In high-end audio, the entire audio chain matters. Often addressing/upgrading the weak link components yields the best sonic upticks.

In order to sonically evaluate an audio component, the rest of the audio chain must be of a high enough quality to hear the differences.  Not enough data to draw any conclusions 

As a matter of principle, it seems to me counter-productive to seek to evaluate a component using other components of a poorer sound quality than the one under evaluation.

But it is more counter-productive to seek to allocate reliable or universal relative sound quality ratings to diverse components.

So the answer is not 'no', but 'the question is not susceptible to a reliable answer'.

There are many cheap mass market products on the market, for example an entry level turntables or speakers, but when it comes to analog playback you can hear the difference upgrading just a cartridge (read above).

Of course if you will start from interconnect cables using such entry level system the difference will be hardly noticeable (if any). 

OP: isn't this:

do I need to wait until I get better speakers to hear the differences of cartridges?

Loudspeakers in an infinite variety of rooms are so varied that evaluating other equipment only has merit in a particular system. There are exceptions, a cartridge that does not track well will break up prematurely and that will apply to all systems. Otherwise clearthinker is right, you can not generalize to other systems. Now if there was a calibration standard that could be applied to audio systems like there is for projectors this could change. This is actually now possible given digital control but would not apply to "analog only" individuals. 
In short, we are very much all alone by ourselves when it comes to evaluating equipment. What sounds great in your system may not be great in others regardless of quality. This is one reason you have to take reviews with a grain of salt. You may also notice that certain brands are always being reviewed by people who are fond of that brand to begin with. Bias has many forms. 
How do you keep from buying equipment that will not work well in your system? In the end you can't. I would bet that many if not most of us have bought equipment we became unhappy with. Our systems evolve slowly over time and we learn what works well with our own situation. Set amps will be worse than terrible with my speakers. I know not to go there. With horn speakers my amps are extreme overkill. There are so many ways to skin this cat. We all have our own ideas of what is best. I do find it interesting that if you have an excellent system evaluated by a number of audiophiles all will agree that it is a fine system. The same will happen with a terrible system. All will agree it is terrible. So there is a standard in our heads even if you can't define it.