In short, yes, the phonetic part may or may not contribute to meaning. But let me put this more precise. I understand that Western readers must have been bewildered by the strange history of Chinese characters. There has been so much misconceptions that I cannot resist to add several remarks.

Abbreviations:

char := Chinese character
p() := pronunciation of *
m() := meaning of *
x ~ y := x is close or related to y
x ~/~ y := x is not apparently close or related to y

Consider char AB consisting of char A and char B sticking together (vertically or horizontally, or stuck in the middle). For our purpose, let char AB be an 形聲 (xíng shēng / Phono-semantic character) char. Without loss of generosity, let char A be the phonetic part, and char B be the semantic part. By our assumption,

p(AB) ~ p(A) ... ... (a)
m(AB) ~ m(B) ... ... (b)

Logically, in our setting, there are these possibilities: (Examples follow shortly)

m(AB) ~ m(A) ... ... (c)
m(AB) ~/~ m(A) ... ... (d)

Before seeing some examples, we naturally wonder, why did this happen? How was the accepted form of AB be agreed on, in the Chinese-using community? And how did these consensus arrive among them at all? You might picture that (along evolution of time):

• Suppose p(A) = P and m(B) = M
• It was intended that a new char X be created with m(X) = M' and p(X) = P', with P' ~ P and M ~ M', but either it happens that m(A) ~ M' (case c) or m(A) ~/~ M' (case d).
• Then elders of the tribe or government officials (??) gathered, to decided how X is written.
• They decided X = AB.
• They announced the decision, and citizens (??) happily accepted.

The process is not only strange-sounding but in fact, wrong. There are two ways how it happened.

—

The first version is 假借 (borrowed homophone). This corresponds to case d above.

• A concept M' with sound P' had already been established in spoken Chinese, but no corresponding char existed.
• Someone (unlikely a she in the patriarchal society) wanted to write down a char X with m(X) = M' and p(X) = P'.
• He made great effort to find a char A with P = p(A) ~ P', but N = m(A) ~/~ M' in general.
• He wrote A, intending m(A) = M' and p(A) =P'.
• From now on, m(A) = N or m(A) = M', depending on context. A is thus overloaded.
• Since so much confusion eventually arose, people started to add another char B with M = m(B) ~ M', that is to say, to coin AB, replacing the second meaning of A. (But Q = p(B) ~/~ P' in general.)
• Thus, p(AB) = P' and m(AB) = M'.

Examples: 莫(Oracle), a picture of setting sun among woods, means "evening". It was borrowed to be the homophone 莫 "not", so 日"sun" was concatenated to it.

父(Oracle), a picture of a sharp tool, means an ax. It was borrowed to be the homophone 父 "father", so 斤 "a small ax" was concatenated to it.

—

Another version is 引申 (figurative meaning). This corresponds to case c above.

• A new concept M' was gradually formed, calling for written expression yet to exist.
• There was the first person who wished to write some X with m(X) = M'.
• He made great effort to find a char A with N = m(A) ~ M'.
• He wrote A, intending m(A) = M', while p(A) =P, as was before.
• Since so much confusion eventually arise, people started to add another char B with M = m(B) ~ M', and to coin AB, replacing the second meaning of A. (But Q = p(B) ~/~ P' in general.)
• Phonology has changed so much that p(AB) = P' ~/~ P = p(A), no longer same, and people do not remember how it was created.

Examples:

冓(Oracle), a picture of a pile of crossed wood sticks, means "to connect, to join". It generated figurative meaning "to talk", so 言 "speech" (a picture of a woodwind instrument) was concatenated to it, becoming "講".

卑(Oracle), a person standing, holding a tablet or plaque (modern sense: inferior, bad), means probably a servant job. It generated figurative meaning "maidservant", so 女 "woman" (a picture of a dancing person) was concatenated to it, becoming "婢".

—

It hardly (if ever) was the case that X = AB came into existence without the intermediate stage of borrowed homophone or figurative meaning. Everything becomes reasonable, doesn't it!

—

ref.: Some of them comes from my memory, sorry. Some books I once borrowed or read are not at hand, but I cite one book I have, 許進雄《簡明中國文字學》(台灣新北市:學海出版社,2000).