Yes. If basic assembler.

No. If you're going to implement an assembler that supports constants and symbols which can be combined into expressions. And expressions can easily be parsed for example[0]:

    〈primary expression〉->〈constant〉|〈symbol〉|〈local operand〉|@|
                        (〈expression〉)|〈unary operator〉〈primary expression〉
    〈term〉->〈primary expression〉|〈term〉〈strong operator〉〈primary expression〉
    〈expression〉->〈term〉|〈expression〉〈weak operator〉〈term〉
    〈unary operator〉-> + | − | ~ | $ | &
    〈strong operator〉-> * | / | // | % | << | >> | &
    〈weak operator〉-> + | − | | | ^

Your code might be hard to read if you'll not create a parse tree for it.

[0] - http://www.mmix.cs.hm.edu/doc/mmixal.pdf

> Huh? Parse tree for assembly?

Why not? The structure you need to represent something like

    lea eax, [eax + eax * 4]

is tree-shaped. It's not as general as many other parse trees, since you don't have arbitrary nesting. But it is a tree-shaped thing that represents a parse, and if you need a name for it, "parse tree" is reasonable. The list containing all the labels/instructions/whatnot in the program is also a trivial tree.

(I'm aware that RISC-V addressing modes are probably simpler than the x86 example above.)

Only if you want a crude Assembler, if you want something like MASM/TASM, then one needs definitely a proper parser.