No, correct sound is 밥 bab 머거써? meogeosseo? you should say it clearly one bye one. However, if somebody say like 밤, In case s/he say it quickly or without break. Because 밥 is end ㅂ and 먹었어 start ㅁ. It's called 자음동화(Consonant Synchoronization) which make pronounce Korean more easily.

Actually, "밤 머거써" (밤, not 밥) is the standard pronunciation. To pronounce ㅂ coming before ㅁ accurately, you need to insert a substantial pause which would be very unnatural and impractical. So in nearly all cases, it is pronounced as 밤 머거써. The reason for this is because of the "unreleased" nature of most Korean consonants. When consonants such as ㄱ,ㄷ,ㅂ,ㅅ,ㅈ, etc. comes at the bottom (받침) and is not followed by a vowel (ㅇ) in the next syllable, the sound is muffled (ㅂ,ㅃ,ㅍ are indistinguishable, for example). While the ending(받침) ㅂ sounds like the English p, it doesn't have p's light puffing of air at the end. This makes the sound dull and unclear, and makes it degenerate to an ㅁ(m) sound if the subsequent consonant is ㅁ or ㄴ. To illustrate, if you say "Bop must go" sloppily, it can sometimes come out like [Bommustgo]. Although it is much more rare because English p is correctly articulated, it shows that p can easily become to m which is an easier sound with a similar lip formation. To verify it, you can look up words with a ㅂ-ㅁ sequence in it (밥 먹다 is a two word phrase, so it won't be in the dictionary). For example, Naver lists the pronunciation of 겁먹다 as "검먹따", not "겁먹따". 밥 먹다 works exactly the same way in this respect, even though it's not a single word - written word spacing seldom affects the pronunciation as no one thinks about it when they speak. Other examples are 감사합니다 becoming 감사함니다 (ㅂ-ㄴ case), and 밥맛 becoming 밤맛. All these are standard pronunciation listed as such in the dictionary, because you can't make the original sound without a big, unnatural pause.

I guess it varies from person to person. Sometimes it sounds more like 밤, sometimes 밥