Is function argument required to be enclosed in a <mrow> tag?

No, function argument is not required to be enclosed in a <mrow> tag. Consider the following cases:

1. Parentheses Omitted - If parentheses are omitted, <mrow> is not recommended. Adding it has no presentation impact:

<math><mi>sin</mi><mo>⁡</mo><mi>ω</mi><mi>t</mi>
  <mo>,</mo>
  <mi>sin</mi><mo>⁡</mo><mrow><mi>ω</mi><mi>t</mi></mrow></math>
    $\sin \omega t,\sin \omega t$

2. Parentheses Required with Single-Term Argument - If the argument is a single term, <mrow> is not recommended. Adding it inside or outside the parentheses, or both, has no presentation impact:

<math><mi>f</mi><mo>(</mo><mi>x</mi><mi>y</mi><mo>)</mo>
  <mo>,</mo><mi>f</mi><mo>(</mo><mrow><mi>x</mi><mi>y</mi></mrow><mo>)</mo>
  <mo>,</mo><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mi>y</mi><mo>)</mo></mrow>
  <mo>,</mo><mi>f</mi><mrow><mo>(</mo><mrow><mi>x</mi><mi>y</mi></mrow><mo>)</mo></mrow>
  </math>
    $f\left(xy\right),f\left(xy\right),f\left(xy\right),f\left(xy\right)$

3. Parentheses Required with Multi-Term Argument - If the argument has multiple terms, <mrow> is not recommended. Adding it inside or outside the parentheses, or both, has no presentation impact:

<math><mi>cos</mi><mo>(</mo><mi>ω</mi><mi>t</mi><mo>+</mo><mi>a</mi><mo>)</mo>
  <mo>,</mo><mi>cos</mi><mo>(</mo><mrow><mi>ω</mi><mi>t</mi><mo>+</mo><mi>a</mi></mrow><mo>)</mo>
  <mo>,</mo><mi>cos</mi><mrow><mo>(</mo><mi>ω</mi><mi>t</mi><mo>+</mo><mi>a</mi><mo>)</mo></mrow>
  <mo>,</mo><mi>cos</mi><mrow><mo>(</mo><mrow><mi>ω</mi><mi>t</mi><mo>+</mo><mi>a</mi></mrow><mo>)</mo></mrow>
  </math>
    $\cos (\omega t+a),\cos \left(\omega t+a\right),\cos (\omega t+a),\cos \left(\omega t+a\right)$

⇒ Function Arguments - U+2061 and "mrow" Tag

⇐ Function Arguments - Parentheses and Spacing

⇑ ISO 80000-2 Quantities and Units - Mathematics

⇑⇑ MathML (Mathematical Markup Language)