I have heard that Srila Bhaktisidhanta told once (most probably in a mood
of a manjari) that we as devotees (in this line) do not have anything to do
with Krsna, and that we are connected with Krsna only because Radha has
a relation with Him.
If one becomes a cowherd boy, is he (according to this logic) more on the
side of Krsna and Balaram, or?
This is more a statement of bhava that one will agree or disagree with based upon bhava. Whether you think of yourself as exclusively a servant of Radha or Krsna depends upon the strength of your bhava. However, even apart from bhava we understand in tattva who is the object of God's love. Who is more important, god, or gods servant? It could be thought of many ways. Don't forget that some sakhas long to serve both Radha and Krsna by assisting their romantic union.
I don't have bhava but I root for Krishna and Bala.
Sri Rupa writes about these priyanarma sakhas thus.
"Carrying messages among the young women of
Vraja, encouraging the gopis’ love for Krsna, taking Krsna's side
when the gopis are present and Krsna is not present, showing
skill at siding with the chief gopés when Krsna is present but
the gopis are not, and arguing intensely by whispering in each
others ears, are the activities of the priya-narma-sakhas."
Sri Jiva comments,
"Pranaya-gamita means “being sympathetic to their love.” When
Krsna engages in various pastimes with the gopis, the priyanarma-
sakhas side with Krsna when the gopis are present and
Krsna is not. When the gopis are not present however, and Krsna
is present, they are skilful in siding with the gopés heading the
various groups. It should be understood that if both Krsna and
the gopés are present, they take Krsna's side."
So overall the gopas' unlimited affection for Krsna is greater than their unlimited affection for Radha, as opposed to Radha's dasis whose position is the reverse. And the object of the gopa's love is Krsna Balarama, as opposed to Radha Krsna. But the priyanarma has both a yuktesvara and yuktesvari, both a male (sakha) and female (sakhi) group leader. So they in particular are involved in tending to Radha and Krsna on occasion. Sarupa (Gopa Kumara) of Sanatana Goswami's Brihat-bhagavatamrta, a priyanarma cowherd, expresses more joy is getting Radha's order than cowherding with Krsna. However, his joy is based on the knowledge that by pleasing Radha, Krsna will be more pleased with him. So even the priyanarma is krsna snehadhika, he has more affection for Krsna. We also find Prabhupada in his "Prayer to Lord Krsna" seeking to please Radha for the sake of pleasing Krsna. Still we also read from the pen of Sanatana Prabhu that Sarupa was ordered by Radha to enlighten "her devotee," the Mathura brahmana that Sarupa (Gopa Kumara) became the guru of, who also developed sakhya rasa. So be it. Jaya Radhe! Jaya Ram Govinda!