Let's assume that the collateral rate on cash equals the overnight rate, that we have a schematic (lined/tiled up accrual periods and payments dates) strip of dates/times $T_0<T_1<\ldots <T_n$, accrual factor $\tau_t := \tau(t-1,t)$, and $c_t$ collateral rate at $t$ (overnight $t-1$ to $t$).
The floating coupon is then:
$$ \prod_{s=T_{i-1}}^{T_i}\left(1+\tau_sc_s \right) -1. $$
Let's further assume that we can live with approximating daily compounding by continuous compounding:
$$ \prod_{s=T_{i-1}}^{T_i}\left(1+\tau_sc_s \right) -1 \approx \mathrm{e}^{\int_{T{i-1}}^{T_i}c_sds} -1. $$
Then the time-$0$ present value of this strip of floating coupons is:
$$\sum_{i=1}^n \mathbf{E}^Q\left[\mathrm{e}^{-\int_{0}^{T_i}c_sds} \left(\mathrm{e}^{\int_{T{i-1}}^{T_i}c_sds} -1 \right)\right] = \sum_{i=1}^n \left( \mathbf{E}^Q\left[\mathrm{e}^{\int_{0}^{T_{i-1}}c_sds}\right] - \mathbf{E}^Q\left[\mathrm{e}^{\int_{0}^{T_{i}}c_sds}\right]\right) $$
$$ = \mathbf{E}^Q\left[\mathrm{e}^{\int_{0}^{T_{0}}c_sds}\right] - \mathbf{E}^Q\left[\mathrm{e}^{\int_{0}^{T_{n}}c_sds}\right], $$
that is, the difference of collateralized discount factors at stub time and last payment time (under assumptions made, we do have the 'telescopic' effect that makes FRN's 'at par').
Note: Let current time be $T_j$ (we are inside the strip timeline, not before it; $j\geq 1$). Under assumptions above, $T_j$ is also the fixing date (or rather the publishing date of the compounded index based on already fixed overnight rates) of the value of the $j$-th floating coupon. The current PV of the residual floating coupon strip will be:
$$\sum_{i=j+1}^n \mathbf{E}^Q\left[\mathrm{e}^{-\int_{T_j}^{T_i}c_sds} \left(\mathrm{e}^{\int_{T{i-1}}^{T_i}c_sds} -1 \right)\right] = \sum_{i=j+1}^n \left( \mathbf{E}^Q\left[\mathrm{e}^{\int_{T_j}^{T_{i-1}}c_sds}\right] - \mathbf{E}^Q\left[\mathrm{e}^{\int_{T_j}^{T_{i}}c_sds}\right]\right) $$
$$ = 1 - \mathbf{E}^Q\left[\mathrm{e}^{\int_{T_j}^{T_{n}}c_sds}\right]. $$
Note 2: If this strip of floating coupons were part of an FRN, we would add one extra cash flow to it at $T_n$ consisting of the reimbursement of the principal (set to $1$ here) of the note. So the PV of the extended strip would then show the strip being 'at par':
$$ 1 - \mathbf{E}^Q\left[\mathrm{e}^{\int_{T_j}^{T_{n}}c_sds}\right] + \mathbf{E}^Q\left[\mathrm{e}^{\int_{T_j}^{T_{n}}c_sds} \cdot 1\right] =1. $$
Note 3: Under the same assumptions, time-$0$ par swap rate is then:
$$ K = \frac{P^{ois}(0,T_0) - P^{ois}(0,T_n)}{\sum_{i=1}^n \delta_i P^{ois}(0,T_i)},$$
where $P^{ois}(0,T):= \mathbf{E}^Q\left[\mathrm{e}^{-\int_{0}^{T}c_sds}\right]$, $\delta_i=\tau(T_{i-1},T_i)$.
