Generally, double consonants are not pronounced distinctly in English, unless they are part of different syllables and the emphasis is on the second syllable.
A word like dissatisfied is formed by adding a prefix dis- to the word satisfied. It starts off with two s in separate syllables, and can be pronounced like that- one at the end of the first syllable, one at the end of the second syllable.
A word like irregular is formed by adding a prefix in- to the word regular. The n-r combination is difficult to say, so we replace the n by another r. The same thing happens with the letter l, so in + licit becomes illicit. According to Cambridge Dictionary, the first l is not pronounced, likewise with in + modest. Note that this conversion only happens with word that passed through medieval latin: more modern words like inroad (1540), inlay (16th C) and inline (1913) are unaffected.
The same kind of conversion happens in arabic for sun letters (il+r -> irr). In arabic double consonants are always clearly pronounced, and this applies to sun letter conversions too.
In a non-rhotic dialects there is an identifiable reaason for not pronouncing the first r, because in non-rhotic dialects (England english, for example) an r followed by a consonant is not pronounced.
In rhotic dialects such as US english, the pronunciation of the n-become-r is, according to Merriam-Webster, optional.
I am a native of England (non-rhotic) and I do not pronounce it as a double r. I can and do double the r when speaking arabic, so I do understand the difference. Other natives of England do not pronounce the double r. If I heard somebody pronounce it with a double r, I would assume that they were foreign. I believe that I have heard natives of Scotland (rhotic) pronouncing it with a double r. I cannot comment on US english.
Here are recordings of me saying irregular and erectile:
And here I say irregular again, pronouncing the two r's separately.
As James K said, this doesn't have anything to do with the spelling.
Different accents of English have different patterns for the use of "dark l" vs. "light l". As you mentioned, some accents are even described as having only one of these sounds. Accents with "both" sounds are often described as actually having a "gradient" of "darker" vs. "lighter" /l/s in different environments. So this is a pretty complicated question.
In general, there seems to be a tendency for "dark l" sounds to be used more often in American accents than in British accents.
In the British "Received Pronunciation" accent of English that is often taught to learners, "light l" is used before a vowel sound, even when the /l/ comes at the end of a word or after a stressed vowel. This accent would have "light l" in "killer", "bellicose", and "pullup". (I don't know if the "light l" in "pullup" might be a bit darker than the light l used in other contexts; that sounds somewhat plausible to me.)
In certain American English accents, "dark l" is used before consonants, and also word-finally, even when a vowel follows, but "light l" is used before a vowel in most word-medial contexts. These accents would have "light l" in "bellicose", but because "pullup" is a compound, I think it might have dark l. I'm also not sure how words like ""killer" are treated in these accents.
In other American English accents (like mine), it seems that "dark l" is used whenever the /l/ is not at the start of a metrical "foot" (either as the very first sound, as in "lucky", or as an element of the onset cluster in the first syllable of the foot, as in "climbing"). So I have "dark l" in killer, bellicose and pullup because the /l/ is not at the start of a foot, but I have "light l" in words like illiterate, illuminate, crystallography, collect where the /l/ is at the start of a stressed syllable.
I quoted some sources in my answer to a related ELU question: L in the middle of a word: dark l or light l?
Best Answer
It's a common misunderstanding to think that the way a dictionary divides headwords is supposed to indicate the syllabification of the word. It doesn't; it's related to the syllabification, but not the same. What it's meant to indicate is where a word can be broken for hyphenation.
You can find more explanation of this in the answer to the following ELU question: Different syllabic boundaries in various dictionaries?
Actual phonetic syllabification is also complicated. Certain words are easy to divide into syllables (e.g. "hangnail" should clearly be divided as /hæŋ.neɪl/) but many others are more difficult. Different scholars have different theories about how to divide words like "barrel", "mattress", "later" and "selfish". John Wells proposed syllabifying these as /bær.əl/, /mætr.əs/, /leɪt.ə/ and /sɛlf.ɪʃ/ respectively.