No, padding would make the message much easier to crack. This is a great example of why cryptography is left to the professionals (I am not a professional cryptographer, I'm not even a very good amateur one). Amateurs tend to just make things worse.
First problem is the Enigma had no way to produce a "null". It was only capable of producing letters.
The nearest equivalent of your scheme would be to pick a letter to use as padding (for example,
A) and then add that at the start of the message. Yes, it makes it a bit harder to find the
KEYKEY repetition, but not much. You just need to slide your window of six characters over a bit and cryptographers were already doing such sliding window analysis to find other cribs.
But because it's always the same letter at the start of the message it gives the cryptographer a very reliable crib.
(For this answer I'm ignoring the plugboard and rings, there were other techniques to work those out).
Let's say the Germans always put at least two padding letters before the key. And let's be generous and say they choose a different padding letter every day. Now the cryptographer knows at least the first 2 letters are going to be the same letter, and there's a very good chance the next letters are also the same. This provides the cryptographer with a very small set of possible texts to work through. Since they're right at the start of the message, they can reveal the rotor settings.
Now any setting can quickly be eliminated if decryption does not result in a message which starts with at least two identical letters.
It doesn't even do a very good job at masking the key, since it's still known that the repeated key will start somewhere in the first N characters (where N is the maximum amount of padding the Germans use). It adds, at most, N - 1 more possibilities.
A A K E Y K E Y
A A A K E Y K E Y
A A A A K E Y K E Y
...and so on...
This is not worth the cryptography gold that is the padding.
The British decrypted the German enigma because they knew that they would repeat the message key twice at the start of every message.
While this was the first and most important crib, and it was found by the Poles, different branches of the German government and armed forces had different procedures for using the Enigma which changed over the war. This flaw did not last long. For example, by 1937 the German Naval Enigma had already rectified this flaw but was cracked anyway.
Key repetition was just one of many the Poles and British had available to them. "Pinches" (stealing code books) were one, but the most reliable was the methodical Germans themselves.
The cryptographers knew, for example, that certain operators would always end a message with
H E I L H I T L E R, or begin a weather report with the same phrasing, or that somewhere in the message would appear the name of their unit, or location, or any number of other likely texts.
The operators also provided their own cribs. The person encrypting the message had to come up with a key. Humans are very bad at producing randomness. A radio operator, possibly in the field, possibly tired, hungry, cold, has to come up with dozens of unique keys every day. They're going to get sloppy. The cryptographers could use this to guess what the key is likely to be, or eliminate unlikely keys (for example, it's not going to be
Furthermore, they could identify individual radio operators by how they transmitted their Morse Code, known as a "fist". Certain operators would have certain ways of picking their keys, or certain ways of writing their messages to provide cribs, and the cryptographers could use this to their advantage.
The Enigma machine had other mathematical flaws which were exploited. Rather than going into them here, I recommend Numberphile's excellent videos on the subject.
In addition Simon Singh's book on code breaking, "The Code Book".