Does 下 in 吃不下饭 convey any meaning? 我们着急得吃不下饭，睡不好觉。

I understand that 好 in 睡不好觉 adds the meaning of &quot;well&quot;, so &quot;sleep well&quot; instead of &quot;sleep&quot;, but does 下 in 吃不下饭 change anything?
Yes it does.
I won't go into the details of your textbook example. It may not be the best one because in that sentence the 下 could probably be replaced by some other result complement and roughly keep the same translation in English.
Generally speaking, 下 as a result complement often has the meaning of fitting or containing (the potential complement as in &quot;V 得 Res.&quot; and &quot;V 不 Res.&quot; constructions is similar to the result complement).
Some examples:

他车子能坐下5个人 (= his car can accommodate 5 people)


电梯里站得下10个人 (= ten people can fit in the elevator = the elevator can contain ten people)


这个箱子太小了，装不下这么多衣服 (= this box is too small, it can't contain so many clothes)


我吃不下饭 (= I can't eat any more = I can't fit any more food in my stomach, or, my stomach can't contain any more food)

As additional proof of the semantic value of 下 in this construction, you can replace it with another result complement to a different effect:

我吃不了饭 (= I can't eat = meaning that something is preventing you from doing so, instead of your stomach being unable to eat more, e.g. 今天我工作太忙，吃不了饭)