Watts Engineering labs

All coax fed antennas generate some level of common mode current on the coax shield.  This current reduces the current that actually gets to the antenna and thereby reduces signal strength on both transmit and receive.  Common mode current flowing on the shield can also cause RFI and increase your noise floor on receive.  

But if you are NOT experiencing RFI, then you may be able to operate satisfactorily without any Common Mode Chokes in your system.  The gain and pattern of your antenna will still be changed by whatever common mode current there is (because the shield is radiating), even if it is not large enough to cause RFI.  But if you are happy with the antenna's performance and you have have no RFI problems, then you could be fine without any Common Mode Chokes.

If you have no RFI problems, then the issue of whether or not Common Mode Chokes are needed comes down to "what type of operator or person you are".  If you are a minimalist, then you can get by without a choke.  However, if you are the sort of person who wants the best possible performance of your station (within reason), then the use of Common Mode Chokes is generally considered essential.  

Absolutely, assuming that the chokes are good enough on the frequencies of interest.   

A Common Mode Choke must present a high impedance to common mode current.  This "encourages" current to flow in the antenna rather than on the outside surface of the coax shield.  

There are two "figures of merit" that one can look at to determine whether or not a particular Common Mode Choke will effectively eliminate RFI:

1) Common Mode Rejection Ratio (CMRR), and

2) Choking Impedance.

A choke with higher CMRR (on the frequencies of interest) will always outperform one with a lower CMRR.  

A choke with higher choking impedance (on the frequencies of interest) will almost always outperform one with lower impedance.  

Some people worry that these metrics are dubious because they are measured in labs in (generally) 50 ohm impedance systems.  This does not matter, these metrics are still highly useful for comparing chokes.

The actual CMRR of the overall antenna system will likely not be the same as the CMRR of the choke itself.  However, a better choke (higher CMRR) will outperform a lesser choke.

Much the same can be said about choking impedance:  the overall antenna system impedance will be changed when a choke is inserted in the system.  In general, the higher the choking impedance the less the overall system is affected.  

CMRR and choking impedance are not independent.  If one is higher, then so will be the other one.  They are just two ways of measuring the effectiveness of the inductor that is the Common Mode Choke.

The answer is a firm "maybe".  

If you are experiencing RF Interference (RFI) then it is entirely possible, or even highly likely, that your coax is also picking up local noise from household devices. If your household does not have any noisy devices, such as switching power supplies or LED lighting, or dimmers, or variable speed electric motors (usually on HVAC systems), then this won't matter since there is no noise to pick up. Unfortunately, this is an unusual situation in today's world. Most modern electronic products use switching power supplies, some of which generate electrical noise. Even USB phone chargers can cause a lot of noise. The units made by Apple and Samsung are quite quiet. But the inexpensive third party ones made in China can be very noisy.

Local noise gets into your receiver via the same path that causes RFI, namely common mode current flowing on the coax shield.  This is why you may not have a noise problem if you don't have an RFI problem.

However, it is possible that noise can be picked up on the coax shield, and raise your noise floor, even if you are not experiencing RFI.  This happens when no chokes are used to choke off common mode current but your household happily has no devices that are sensitive to RFI.  The RFI is there, it's just not causing any problems.  But this means local noise can induce common mode current on the coax shield and get into your receiver.