Thieves' Cant isn't a written language, thus there would be nothing to understand via a spell.
Nowhere in the quote you've pulled (or the PHB) is thieves' cant ever described as a written language. This is because thieves' cant is both verbal and physical communication. Some word substitution (1 to 1) is used, but it is largely based on metaphor and contextual meaning and a big part of this is the hand symbols used when speaking. D&D's basis for thieves' cant is both historical and a trope.
The symbols mentioned are more like pictographic signs than words.
As such they are not translated, but identified, similar to how we use symbols such as the biohazard sign and nuclear sign to signify specific danger or how the symbols on a crosswalk signify when to wait and when to go. The closest living example of this I can highlight would be Hobo symbols that survive and are still in use today in the US. Different symbols would mean different things to different groups and insider knowledge for understanding thieves' cant symbols would be a must.
No, because the point of Thieves' Cant is that observers can't tell it's being used. The conversations being lengthy isn't a giveaway either, since that just means that the conversations the messages hide in are normal length and the Cant message is ¼ the length of the carrier message. For longer Cant messages, just talk more about mundane things like your sister's guild training or that horse you were admiring in the last town.
But even if we assume (or it's been house-ruled) that a listener can tell when Cant is and isn't being used, just not what the message is…
Still no, not if they're using Thieves' Cant properly. To use Thieves' Cant properly, you have to use it all the time with your fellow rogues, just as part of normal casual conversations with them, so that even if someone twigs that the conversations are “not normal”, you don't give away why you're using Cant by presenting an obvious pattern. If the only time a pair of rogues use Thieves' Cant is when they're up to no good, even the most Lawful Stupid paladin can figure out that “unusual conversations = I should start interfering!”
When it's used all the time between the two rogues, even someone who has learned to recognise the use of Cant won't be able to tell that they're up to mischief. It's definitely not grounds for making intuition checks or anything to figure out that something is up. When every conversation between the rogues is “not normal”, then it stops being suspicious.
Part of the point of Thieves' Cant is that knowing that there's a secret meaning is not the same thing as knowing that there's an important secret meaning. Two rogues bantering using Cant could as easily be talking about inconsequential things — ribbing each other, cracking jokes, discussing last night's hangover — as they could be talking about real plans. When all the talk between two rogues is laced with impenetrable jargon and slang, nobody can tell when to be concerned and when it's innocent.
The same principle is observed in modern cryptography — if you only encrypt sensitive messages, then anyone monitoring you knows when you're discussing sensitive topics and can probably figure out the message based on context, like time, other activity, and receiver.
Thieves who speak in Thieves' Cant only when they're discussing doing something improper aren't very good at being thieves.
Best Answer
No.
Comprehend languages only lets you understand the literal meaning of the words.
Thieves cant states that the message is coded so only thieves would understand.
So while you may understand the literal message, "The rooster flies when the blood moon rises," you will not understand that this means that, "The man with the red scar on his neck is your target for assassination by midnight tonight."
This is akin to telling somebody to read the 3rd letter of the first paragraph in a book, in which it spells out a secret message to them. Comprehend languages would let you understand the paragraph, but would give you no insight whatsoever to the hidden code inside it.