They would be allowed to serve unless expelled. However, under House rules, once indicted for a crime for which a sentence of two years or longer may be imposed, a representative should resign from any committee or party caucus position they may hold, and upon conviction, refrain from voting until either the conviction is quashed or the representative is reelected. There are no automatic penalties for merely being arrested.
According to the CRS report Status of a Member of the House Who Has Been Indicted for or Convicted of a Felony, last updated in 2014, there are no penalties for a representative indicted for a felony, either under the Constitution, statutory law, or the Rules of the House. However, this is slightly out of date, as beginning in the 116th Congress, the rules package for the House of Representatives have changed to include provisions relating to members indicted for a felony, as well as convicted:
(a) A Member, Delegate, or Resident Commissioner who has been convicted by a court of record for the commission of a crime
for which a sentence of two or more years' imprisonment may
be imposed should refrain from participation in the
business of each committee of which such individual is a
member, and a Member should refrain from voting on any
question at a meeting of the House or of the Committee of
the Whole House on the state of the Union, unless or
until judicial or executive proceedings result in
reinstatement of the presumption of the innocence of such
Member or until the Member is reelected to the House after the date
of such conviction.
(b) A Member, Delegate, or Resident
Commissioner who has been indicted for or otherwise
formally charged with criminal conduct in any Federal, State, or
local court punishable as a felony for which a sentence of two or
more years’ imprisonment may be imposed should resign from
any standing, select, joint or ad hoc committee, and any
subcommittee thereof, on which such Member, Delegate, or
Resident Commissioner serves, and should step aside from
any party caucus or conference leadership position such
Member, Delegate, or Resident Commissioner holds, unless
or until judicial or executive proceedings result in acquittal
or the charges are dismissed or reduced to less than a
felony as described in this paragraph.
Rules of the House of Representatives - 117th Congress - Rule XXIII
The report also notes, however, that "There is no express constitutional disability or “disqualification” from Congress for the conviction of a crime, other than under the Fourteenth Amendment for certain treasonous conduct". As a result, the only way in which a representative would be expelled for such an offence is as provided in the Constitution:
Each House may determine the Rules of its Proceedings, punish its
Members for disorderly Behaviour, and, with the Concurrence of two
thirds, expel a Member.
US Consitution: Article 1, Section 5, Clause 2
According to Chapter 12, § 13 of Deschler's Precedents, however, this is unlikely to take place until a member's conviction, including any appeals - which would be long after the members' arrest.
Where a Member of Congress has been convicted of a crime, neither
the House nor the Senate will normally act to consider
expulsion until the judicial processes have been exhausted.